Question

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
2(x^2+y^2)^2=25(x^2−y^2)at point (3,1)

Answer 1

what did you get for \(\Large{dy\over dx}\)

Answer 2

well i wasn't sure if i had to do the product rule but i got 8x^3 +4x^2(2y)dy/dx + 8xy^2+8y^3 dy/dx= 50x-50y dy/dx

Answer 3

good\[
4(x^2+y^2)\left(2x+2y{dy\over dx}\right)=25\left(2x-2y{dy\over dx}\right)
\]
rearrange the terms so that you get something like this:
\[
{dy\over dx}={\rm something}
\]

Answer 4

would i have to use the product rule or just distribute

Answer 5

just distribute.

Answer 6

since there are no two functions multiplying, you do not have to use product rule.

Answer 7

im not sure if i did the math correctly but i got dy/dx= 21/608

Answer 8

Who deleted my post lol

Answer 9

\[
{dy\over dx}=\frac{25x-4x(x^2+y^2)}{25y+4y(x^2+y^2)}
\]
and plug in x=3, y=1

Answer 10

is that what you did?

Answer 11

yeah and for that i got 7/ 13 is that correct

Answer 12

positive?

Answer 13

umm no i got -7/13

Answer 14

should be -9/13

Answer 15

maybe i subtracted wrong but yeah you are correct thank you :)

Answer 16

yw

Answer 17

what did you get for the y-intercept,?
what is the equation of tangent line?

Answer 18

for my final equation i got y=-9/13x+40/13