Use implicit differentiation to find the equation of the tangent line?

Question

to the circle (x-3)^2 + (y + 4)^2 = 25 at the point (-1,-1).

Answer 1

(x - 3)^2 + (y + 4)^2 = 25

Differentiate :

2(x - 3)dx + 2(y + 4)dy = 0

Therefore, dy/dx = (3 - x) / (y + 4)

At (-1, -1),. dy/dx = [3 - (-1)] / (-1 + 4) = 4/3

Let tangent equation be : y = mx + b

Substitute m = 4/3, x = -1, y = -1 giving :

-1 = (4/3)(-1) + b, so, b = 1/3.

Equation of tangent line at (-1, -1) is : y = (4/3)x + 1/3