Question

Find the equation of the tangent line to the curve (a lemniscate) 2(x^2+y^2)2=25(x^2−y^2) at the point (−3,1). The equation of this tangent line can be written in the form y=mx+b where m is:

Answer 1

2) whre b is

Answer 2

Find y', evalute it at your point to get the slope of the tangent line at the point of interest.
Write the line in point-slope form, convert to slope-intercept form.

Answer 3

Do i need to caculate the equation then find y'?

Answer 4

What do you mean?

Answer 5

do i need to simplif first

Answer 6

Differentiate implicitly. Do your simplification when you are trying to isolate y'.
It's not that messy

Answer 7

is the first part: 2(x^2-y^2)2? If so, that's the same as saying 4(x^2 - y^2) @Dodo1
Unless you made a typing mistake..

Answer 8

I assumed that it's squared because lemniscate

Answer 9

\[f(x)=2(x^2+y^2)^2=25(x^2-y^2)\]

Answer 10

sorry I typed it wrong

Answer 11

So Do i need to similfy than Y'?

Answer 12

or move y first?

Answer 13

Just differentiate implicitly like I said

Answer 14

mmmm how do you do that

Answer 15

Is it product rule that I am going to use

Answer 16

?