Equations of Tangents to Circles (Grade 9) | Part 4 | Grade 9 Maths Series

Equations of Tangents to Circles (Grade 9) | Part 4 | Grade 9 Maths Series | GCSE Maths Tutor

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A video revising the techniques and strategies for completing questions on coordinate geometry when looking at tangents to circles - Higher only (Grade 9)
This video is part of the Algebra module in GCSE maths, see my other videos below to continue with the series focussed on coordinate geometry.
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These are the new revision guides I recommend 💡
Higher - New Grade 9-1 GCSE Maths Edexcel Student Book - Higher (with Online Edition) (CGP GCSE Maths 9-1 Revision) - amzn.to/366PltG
Foundation - New Grade 9-1 GCSE Maths Edexcel Student Book - Foundation (with Online Edition) (CGP GCSE Maths 9-1 Revision) - amzn.to/2PpbjBF
Revision videos:
The Entire GCSE in Only 2 Hours!! Higher and Foundation Revision | GCSE Maths Tutor - • Everything You Need To...
Everything for a Grade 6-9 in your GCSE Maths Exam! Higher Maths Exam Revision | GCSE Maths Tutor - • Everything for a Grade...
All The Topics You NEED To Know For The 9-1 Maths GCSE 2020 (Higher) - • All The Topics You NEE...
More videos in the Coordinate Geometry series:
All of Algebra in just over 1 hour!!! - • All of Algebra in just...
Part 1 - Equation of a Line - • Equation of a Line (St...
Part 2 - Perpendicular Lines - • Coordinate Geometry - ...
Part 3 - Equation of a Circle - • Coordinate Geometry - ...
Part 4 - Tangents to Circles - • Equations of Tangents ...
Part 5 - Velocity-Time Graphs - • Velocity-Time Graphs -...
Part 6 - Quadratic, Cubic & Reciprocal Graphs - • Drawing Quadratic, Cub...
Part 7 - Exponential Graphs - • Exponential Graphs | G...
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Пікірлер: 144

@TheGCSEMathsTutor 4 жыл бұрын

Minor correction - at 14:18 the final answer is y=-1/3x+6 2/3 for some reason I wrote the wrong gradient back in! Who knows why 😂🤦🏼‍♂️ I’m only human!

@archiefostr 3 жыл бұрын

Few haha

@paolasassi5171 3 жыл бұрын

Can you tell me why English people are so obsessed with mixed numbers we never ever use them

@emmanuelvinod4037 3 жыл бұрын

isn't it y = - 1/3x + 6 2/3 Or is the 1/3 x positive?

@SAVIORPAF 3 жыл бұрын

@@emmanuelvinod4037 it is -1/3 he wrote -2/3 thats why he just telling that it isn't -2/3 it is -1/3(he forgets again:) as he is only human😂

@emmanuelvinod4037 3 жыл бұрын

@@SAVIORPAF thanks

@QuaternionPhysics1 3 жыл бұрын

Love these types of questions! Seems difficult on the outside, but when you tackle it step by step, it ain’t too bad, and you get the satisfaction of getting to the answer (if it’s correct that is)

@izzavibe4646 2 жыл бұрын

Quite correct sir

@mantleuk 2 жыл бұрын

For real like the overwhelming happiness of progression I’m so happy

@9I09I90 3 жыл бұрын

i made a playlist of videos you made for myself for revision, thanks a lot!! You have blessed my hopes of getting a good GCSE and i hope for all the best for you

@TheGCSEMathsTutor 3 жыл бұрын

Efe Kilic Amazing news what a fantastic idea!! So glad to hear it’s working for you and giving you that extra confidence! 😁🙏🏼🙏🏼🙏🏼

@quartz744 Жыл бұрын

What grade did u get??

@farhanafzal4483 Жыл бұрын

@@quartz744 aired

@hawnting_ 3 ай бұрын

@@farhanafzal4483 damn

@loisjean6327 Жыл бұрын

thank you so much! my teacher skimmed over the circle graphs topic and I keep doing past paper questions and they keep coming up and I never understand them! this has really helped thank you!

@sahilaziz5718 4 жыл бұрын

Would you soon start making worksheets based on your videos?

@TheGCSEMathsTutor 4 жыл бұрын

TEAM Bantz!!! I will do when I get to that part, for now the focus is getting all the videos produced 😁 lots to come though!!!

@mrgoatliri6224 2 жыл бұрын

these are very nice, hope they come in my exam

@undercoversummer1232 3 ай бұрын

How did u do?

@mrgoatliri6224 3 ай бұрын

@@undercoversummer1232 221/240

@mathsmadefun6484 3 жыл бұрын

Sir, for the last question could we tidy 8/ root 7 a bit more? By rationalising it? Giving 8root 7 / 7?

@Jacob-rx5ot 2 жыл бұрын

@dravig9973 2 жыл бұрын

Yes you can, because it's the same thing

@pashtunlion459 4 жыл бұрын

Great video! this is the second hardest topic after vectors in my opinion but you absolutely smashed itt!! one question? if that equation to the circle is x^+y^=25 aint we supposed to square root the 25? or are we supposed to just leave it how it is in these types of question involving tangents ?

@TheGCSEMathsTutor 4 жыл бұрын

pashtun lion Completely agree!! Everyone seems to really struggle with these, glad to hear it’s helped though 😁 it’s a good question, the only reason you would need to square root the 25 is if you wanted to know the exact length of the radius, for these questions we are only really concerned with the gradient of the radius so it is not necessary 😁🙏🏼

@pashtunlion459 4 жыл бұрын

@@TheGCSEMathsTutor Thank you so much! you uploading any videos today?

@TheGCSEMathsTutor 4 жыл бұрын

pashtun lion Not today unfortunately, I have been tutoring from 8am to 5:30pm and now I have 120 year 11 exam papers to mark 🤦🏻‍♂️ hoping to get some posted during the week though! 😁🙏🏼

@khattakjarir3399 2 жыл бұрын

sunge chal da wrora

@seducedol7269 2 жыл бұрын

On 37:06 would the answer not be 8 and 2/3 as you have to halve both? I have no clue if I was right it’s just I kept getting the answer 5.3 recurring as my final answer which is equivalent to 8 and 2/3

@ALR_006 2 жыл бұрын

you really are amazing! thank you so much!

@didieravousten314 Жыл бұрын

Hi sir. At 50:20, where the equation is y = [(-3)/(Root7)].x + [(8)/(Root7)], shouldn't we write y = [(-3.Root7)/(7)].x + [(8.Root7)/(7)] to get rid of the roots on the denominator? Thank you very much :)

@MichaelJackson_real 10 ай бұрын

Thakyou so much in was thinking the same thing and I'm so confused what would say is correct

@antonroy415 11 ай бұрын

Can you also put the answer as: y = 3√7 / 7 x + 8√7 / 7 since I rationalised the denominator

@nawfaljafri 3 жыл бұрын

when am I supposed to use (x²+y²=r²) when finding the line in the circle and when do I use dy/dx? because in the previous video when finding the radius, you used the (x²+y²=r²) Pythagoras equation, however, while seemingly finding the same line in this video, you're finding the gradient equation dy/dx; obviously, they're not interchangeable for preference because they both give different answers so when do I use which?

@nawfaljafri 3 жыл бұрын

is (x²+y²=r²) for just the radius of the circle from the centre of it while dy/dx helps us get the perpendicular gradient? and that radius doesn't mean gradient

@coolguy3943 3 жыл бұрын

Hi sir. Which is more simple: mixed numbers or improper fractions? If you got asked to simplify something fully, which would you choose? Eg at 36:36 would it be 50/3 or 16 + 2/3? Also, for 36:36 , I wrote 50/3 units^2, so would the “units” part be correct as we don’t know the specific unit? Thank you.

@enta3325 Жыл бұрын

i think if u were asked to simplify smth fully, an improper fraction would be okay

@yokitokisoki 3 жыл бұрын

why do you flip the gradient to be negative

@ahmD-ce8cr 4 жыл бұрын

At 14:18 isn't it meant to be y=-1/3x + 6 2/3?

@TheGCSEMathsTutor 4 жыл бұрын

Ahmed Mustafa Whoops well spotted! 😂 my bad!!! Thanks for that!

@blackpinklover4746 2 ай бұрын

thanks thats what I was thinking as well.

@ELLIPTICALWR 2 жыл бұрын

for the last one do we not need to simplify our answer by rationalising the denominator or would we still get full marks for putting: y=-3/root7 x+8/root 7

@vghhhj1657 2 жыл бұрын

Nah you gotta rationalise the denominator

@omarrahmankhan8563 2 жыл бұрын

I actually love you man

@eatinsomtin9984 3 жыл бұрын

Please can you explain why at 8:55 the rise/run is -2/5 and not -5/2?

@SAVIORPAF 3 жыл бұрын

Bc the radius was negative means going downwards

@QuaternionPhysics1 3 жыл бұрын

Gradient is change in y/change in x. (2-0)/(-5-0) = -2/5 (2-0=2 and -5-0=-5)

@Ryan-bm8lc 2 жыл бұрын

sir hi why do you divide by 5 at 26:18

@ahmedmustafa4978 4 жыл бұрын

Sir if I encountered this question would the centre of the circle always be at the origin ? And if this is not the case then the steps that I use to find the equation in the tangent, would they be the same??

@TheGCSEMathsTutor 4 жыл бұрын

Ahmed Mustafa At GCSE level yes, if the circle was not centred at the origin you would not be using the equation of the circle at all so it would just be the same process but using the gradient between the different centre and the tangent point in the same way 😁🙏🏼

@ahmedmustafa4978 4 жыл бұрын

The GCSE Maths Tutor And how would I calculate the gradient between the different centre? Would I use Pythagorean’s theorem?

@TheGCSEMathsTutor 4 жыл бұрын

Ahmed Mustafa change in y over change in x, I go over this in the earlier lessons in this series, you would use Pythagoras if you wanted to work out the length of the radius though 😁🙏🏼

@qafrd5487 2 жыл бұрын

@@TheGCSEMathsTutor After Paper 1 idk about this sir

@Rafmee 3 жыл бұрын

I'm doing it with a calculator and I keep getting it wrong :/ I type the fractions in but it gives me a different answer to what you got

@TheGCSEMathsTutor 3 жыл бұрын

Maybe try it non calculator, sometimes the calculator is overused in situations where you may not actually need it 😁🙏🏼

@obliteratrix306 3 жыл бұрын

Probably just simplifieing it for you

@ollierobertson-kurd 2 жыл бұрын

Shouldn’t you rationalise the last question?

@sheilabirling 10 ай бұрын

THANK YOU

@asmaa1853 Жыл бұрын

thank you😊

@bobsham9136 4 жыл бұрын

Wow I didn’t know about that app! Thanks

@TheGCSEMathsTutor 4 жыл бұрын

My pleasure! Once you get to grips with using it it’s brilliant for coordinate geometry, you can also use it for solving simultaneous equations as well to see the graphical solutions! I may do a video on it soon showing what you can do 😁

@bobsham9136 4 жыл бұрын

The GCSE Maths Tutor yeah it sounds amazing. And I must say that the fraction work you did on this video, it’s most likely will be on a calculator paper than non-calculator.

@TheGCSEMathsTutor 4 жыл бұрын

Bob Sham Never rule it out! 😁 Hence why I teach it this way, if you have a calculator there is no challenge at all during those steps, but as I said, I doubt it would appear like that on a non-calculator paper 🤞🏼

@lolllhello7718 4 жыл бұрын

@Bob Sham @The GCSE Maths Tutor What app

@TheGCSEMathsTutor 4 жыл бұрын

Lolll Hello see 26:30 onwards, it’s in the video 🤣

@jav8624 2 жыл бұрын

@23:06 little confusion 5=-4/5+c 5+4/5=c 9/5=c On the video 5=-4/5+c => 54/5=c little confused there Please help.

@erenyeager6668 Жыл бұрын

are we allowed to give them as improper fractions

@ebadrahman1290 2 жыл бұрын

How can it be negative length on the triangle for the radius gradient

@neptunestic Жыл бұрын

Hi Sir, at 20:17 when i type in on my calculator -4 1/4 divided by -1/4 i get the answer of 4 as the x, what am i doing wrong?

@idkatthispoint-s9s Жыл бұрын

8:57 Even though the answer tuns out to be the same as yours at the end, I still have to ask, why is it +5 and not -5 since -5-0 is just -5

@buymeacatplz 5 ай бұрын

i think its because if u look at the graph he drew, to get from (-5,2) to (0,0) you need to take away 2 (-2) and add 5 (+5), as its the perpendicular gradient

@user-hs3le3uu4d 4 ай бұрын

32:16 how did you get 6^1/4 i’m sooo confused ngm i get it!!!!

@todaysyouth7624 3 жыл бұрын

do you have any exam questions on this topic: your video are amazing by the way?!

@oliviachillingworth201 3 жыл бұрын

you should be able to find some on maths genie i thinkkk

@jamesgoldring-maule6036 2 жыл бұрын

great video as always, thanks.

@TheGCSEMathsTutor 2 жыл бұрын

Thank you for the kind words 😁🙏🏼

@jinethweragama1218 2 жыл бұрын

For the last question is it still accepted if I had written the rationalised version of the surds?

@TheGCSEMathsTutor 2 жыл бұрын

Absolutely!!!

@jinethweragama1218 2 жыл бұрын

@@TheGCSEMathsTutor coooool

@fatemehrezaeinia8235 3 жыл бұрын

Brilliant...😊

@edenmcclain3812 3 жыл бұрын

hi sir great videos helps a lot. @34:16 isn't it supposed to be negative 25/4 i'm a little confused

@SAVIORPAF 3 жыл бұрын

No the negative get canceled our by the negative of 3/4

@lola7172 2 жыл бұрын

@@SAVIORPAF but when u move it the 3/4 is positive

@SAVIORPAF 2 жыл бұрын

@@lola7172 its dividing not subtracting (sign changes when we move to other side not when you divide both sides )when we divide the sign got cancelled out

@luangj2866 2 жыл бұрын

thanks

@rayyanabubakar9015 3 жыл бұрын

Great video

@ahmD-ce8cr 4 жыл бұрын

Hi, I just wanted to ask, during the first part of the video where the equation of the circle (x²+y²=r²) is in the question but I see that you don't seem to pay any attention to it. Is it not important/irrelevant?

@TheGCSEMathsTutor 4 жыл бұрын

Ahmed Mustafa It’s not relevant for this particular question no but it is linked into the previous video (part 3) so I thought it was worth mentioning as to how it all links in together! 😁

@user-hs3le3uu4d 4 ай бұрын

20:59 can someone do like instructions on how to answer the question thas the only way i understand bc he did that with the last video😭😭🙏🏽

@adminss728 2 жыл бұрын

GOAT!

@TheGCSEMathsTutor 2 жыл бұрын

Thanks!!

@itszakw2282 2 жыл бұрын

@The GCSE Maths Tutor Do you have to simplify the fractions or can they stay unsimplified. For example at 13:10 i kept it as 2/6 instead of 1/3. Would that be OK? Please answer

@hafidahfatima9418 2 жыл бұрын

I'm pretty sure you have to simplify. It will make you answer the rest of the question faster because you multiplying by a smaller number. Any way I would simplify incase the mark scheme says so

@itszakw2282 2 жыл бұрын

@@hafidahfatima9418 ok cheers :)

@hafidahfatima9418 2 жыл бұрын

@@itszakw2282 😃 😁

@lamiyakhokon890 3 жыл бұрын

can u leave ur ans in improper fraction?

@hanisquared9620 3 жыл бұрын

What would happen if we rationalised the denominator of the gradient at 47:30

@mathsmadefun6484 3 жыл бұрын

nothing u will just have a rational number hah a

@mathsmadefun6484 3 жыл бұрын

lost guy

@aarontasawer5012 3 жыл бұрын

@@mathsmadefun6484 😂😂

@sayeed2713 5 ай бұрын

31:34

@alishbarasool4035 2 жыл бұрын

Would these questions be on Non-Calculator or Calculator papers?

@hanifahmaria1231 2 жыл бұрын

non calculator for edexcel

@kieratsahota6835 4 жыл бұрын

How many Mark's?

@TheGCSEMathsTutor 4 жыл бұрын

Kierat Sahota 5 😂😂😂

@kieratsahota6835 4 жыл бұрын

@@TheGCSEMathsTutor 🤣

@kieratsahota6835 4 жыл бұрын

Bro In every video just tell us how mnay Mark's just for me? Hahah 😅🤣

@TheGCSEMathsTutor 4 жыл бұрын

Kierat Sahota But then I wouldn’t get to have a laugh every time you ask... 😂

@kieratsahota6835 4 жыл бұрын

@@TheGCSEMathsTutor 🤣

@eatinsomtin9984 3 жыл бұрын

Sir, for 26:04 wouldn't the answer be -145/10 as you still have the negative 29?

@eatinsomtin9984 3 жыл бұрын

Sorry sir if your seeing this, just figured that they cancel each out anyways.

@mrgoatliri6224 2 жыл бұрын

for the last question, do you accept 7Y = -3 root 7 x + 8 root 7

@moistbrick9769 Жыл бұрын

@randomacc77777 Жыл бұрын

No how the hell did you get that

@Anna_04 Жыл бұрын

32:46

@mohamadawad8506 3 жыл бұрын

I did the last one and left gradient as it is then got c=3

@lamiyakhokon890 3 жыл бұрын

is this a caculator or non. ?

@fireemperorzuko8756 3 жыл бұрын

Can be on both

@heartiu4713 4 ай бұрын

is 2 root 7 + 2 root 7 not 4 root 7?

@-_Blitz_- 2 ай бұрын

Yeah it is

@alitoto5452 3 жыл бұрын

If the last questions were on the exam, how many marks will they be?

@SAVIORPAF 3 жыл бұрын

I believe 5

@sozhassan3800 3 жыл бұрын

In the exam, how would we know the centre is (0,0)

@t.4861 3 жыл бұрын

Idek...if its not mentioned just assume its 0,0

@idontknowwhattonamethis75h82 2 жыл бұрын

bruv, had me bare cnfused u no. Y is it not - 1/3x at 14:18

@TheGCSEMathsTutor 2 жыл бұрын

Sorry!! Please check the pinned comment 😁🙏🏼

@idontknowwhattonamethis75h82 2 жыл бұрын

@@TheGCSEMathsTutor Dont worry G, provided me bare help anyway

@TheGCSEMathsTutor 2 жыл бұрын

@@idontknowwhattonamethis75h82 So glad to hear that! Let me know how you get on 😁🙏🏼

@mrover2202 2 жыл бұрын

@@TheGCSEMathsTutor can the final question also be y=-3/root7 + 8root7/7

@alitoto5452 3 жыл бұрын

is this the hardest topic in the GCSE?

@tahakarim1901 3 жыл бұрын

Probably not, since vectors are probably a bit more terrifying.

@lolllhello7718 4 жыл бұрын

Do you have an email that I can email you

@TheGCSEMathsTutor 4 жыл бұрын

Lolll Hello I don’t actually use my email account to be honest, how can I help? You can always message me on Insta! 🤷🏼‍♂️

@lolllhello7718 4 жыл бұрын

The GCSE Maths Tutor I do not have ‘Insta’ but I wanted to know if you do tuition PLZ REPLY !!!!!!!!

@TheGCSEMathsTutor 4 жыл бұрын

I don’t currently have time unfortunately as I am fully booked, but I will be looking to set something up online 😁 plus.. it’s a big country, the likelihood is that you’re miles away!

@TheGCSEMathsTutor 4 жыл бұрын

Lolll Hello I’m 3 hours away 🤷🏼‍♂️ unfortunately!!