Question

Find the equations of those tangents to the circle x^2 + y^2 = 52, which are parallel to the straight line 2x + 3y = 6.

Answer 1

let the equation of tangents is 2x + 3y = c
then perpendicular from center of the circle = radius
center  =  (0,0)
|{(0*2 + 0*3 - c)/(2^2 + 3^2)^1/2}| = 52^1/2
|c/13^1/2| = 52^1/2
c = 2*13 or c = -2*13
c = 26  or c = -26 hence equation of tangents 
2x+3y = 26 & 2x+3y = -26