Find the equation of the tangent to circle x² + y² - 6x + 4y - 12 = 0 which is parallel to line 4x +3y +5

Answer 1

you want a tangent with slope -4/3

the circle is

(x-3)^2 + (y+2)^2 = 25
2(x-3) + 2(y+2)y' = 0
y' = -(x-3)/(y+2)

when y' = -4/3, 3x = 4y+17
this occurs at (7,1) and (-1,-5)

The tangents are thus

4x+3y = 6±25