Question

The equation of the tangent line to the curve x^2 + y^2 = 169 at the point (5, -12) is...

Answer 1

First, take the derivative.
Then, evaluate the derivative at (5,-12)
Then, put the slope from the derivative and the point (5,-12) into the point slope form for a line.

Answer 2

I got the slope as -5/6?

Answer 3

I'm thinking of something more like -5/12. Use implicit differentiation.

Answer 4

oh ok. I have that now. So for the next step I pluf in 5 and 12 for x and y?

Answer 5

jk. already did that

Answer 6

sorry, I'm stuck again

Answer 7

With?

Answer 8

"Then, put the slope from the derivative and the point (5,-12) into the point slope form for a line."

Answer 9

Point slope form for a line, with slope m, , going through a point:\[(x_1,y_1)\]
is
\[y-y_1=m(x-x_1)\]

Answer 10

oh,ok. but I still can't seem to get an answer thats one of my options. I got 12y - 5x = -37

Answer 11

Try again, I'm getting something different.

Answer 12

oh ok... I got 12y + 5x = -169

Answer 13

-5x

Answer 14

This is much closer to what I found, though I question your alteration of signs.

Answer 15

well my final answer was 5x - 12y = 169. Is that still wrong?

Answer 16

I end up with 12y+5x=-119, without checking my work, writing it down, etc...so it may be wrong.

Answer 17

looking over this conversation, you used slope as -5/12 but I used 5/12 b/c isnt y' = -x/y? and -5/-12 = positive?

Answer 18

Absolutely. Yet again, I left out a negative in my original derivative. I really should just get some sleep.

Answer 19

ok, well at least I know the process now. I can check my work. Thank you for your patience!

Answer 20

C'est rien.