Question

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

Answer 1

find y' through implicit differentiation
can you do that?

Answer 2

\[2x+2y(dy/dx)=0\]

Answer 3

then solve for \[dy/dx\]?

Answer 4

and then dy/dx is the slope right?

Answer 5

right, sorry for the late reply

Answer 6

the use that in point-slope form\[y-y_1=\frac{dy}{dx}(x-x_1)\]

Answer 7

Actually, one can do this problem by a student who has not seen derivative yet.

Answer 8

The point A=(5,-12) is on the circle x^2+y^2=169.
The line AO has slope -12/5 then the slope of the tangent at A is
5/12
The equation of that tangent to the circle at A is
y = 5/12(x-5) -12