maths
posted by nanuna .
Find the equation of the tangent to circle x² + y²  6x + 4y  12 = 0 which is parallel to line 4x +3y +5

you want a tangent with slope 4/3
the circle is
(x3)^2 + (y+2)^2 = 25
2(x3) + 2(y+2)y' = 0
y' = (x3)/(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