Tangents to Implicit Curves : ExamSolutions

Tutorial on tangents to implicit curves.
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[@mohamedabdul708]

Thank you very much, you are an amazing teacher. Keep up

[@bob1city112]

lavely video mate

[@MyBuxbunny]

Thank you, I finally get it :)

[@osamarattu]

hey thanks for this

[@al-anoud-123]

for the factorising bit we could do dy/dx(2y-2y+2x)=6x so the 2ys would cancel out and we will end up with dy/dx=6x/2x and the answer is 3

[@ExamSolutions_Maths]

@themanyogi Cool

[@fairyda8690]

As usual,your video is of great help :) But I've got a question...if i'm asked to find the eq. of the tangent in the form ax+by+c=o,how should i proceed? :/

[@bennybenson4642]

You'll get the equation of the tangent in the form y=mx+c then, from there, you'd subtract y from both sides to get 0= mx - y + c
5 years later...

[@-MichelleM]

I need help, please!
1 a) Show that the origin lies on the curve e^x + e^y=2
1 b) Differentiate the equation with respect to x and explain why the gradient is always negative.
For 1b) I differentiated the equation and got -e^(x-y). I cant figure out how to explain why the gradient is always negative.
2) Consider the curve y^3 = (x-1)^2
2 e) By making the substitution x = 1+X, and examining the resulting equation between y and X, show that the curve is symmetrical about the line x = 1 (I made the substitution and got y^3 = X^2. What next?)
Please show the steps! Thank you!

[@ExamSolutions_Maths]

@5524428 Thank you

[@rager7777]

sir, why didnt you simplyfy the dy/dx equation by cancelling off the y's?

[@ExamSolutions_Maths]

Because y is not in every term.

[@rager7777]

ExamSolutions
thank you

[@georgehenna]

y^2 - 2xy = 3x^2 ( + x^2 to both sides )
y^2 - 2xy + x^2 = 3x^2 + x^2 = 4x^2 ( simplify both sides )
( y - x )^2 = ( 2x )^2 ( square root both sides )
y - x = 2x (add x to both sides )
y - x + x = 2x + x ( simplify both sides )
y = 3x
Is there any logic in my working or is my answer a fluke? Thanks.

[@ExamSolutions_Maths]

It is a fluke! Interesting idea though.

[@georgehenna]

Thank YOU!!!!!!!!!

[@mishasalykova8482]

sorry but m (gradient) should be -3 instead of 3 as 3(x-y)/ -(x-y)

[@EpicEditsBySaz]

What??

[@toyahan7195]

How?

[@leen8175]

I think your mistake is that you cancelled 2y in the numerator by the 2y in the denominator, which is Wrong in math