3rd condition to determine a Circle

Question

What is the equation of a circle touching the lines 2x-y-11=0 and +2y+2=0 and having its center on the line 4x+y-27=0
Ans:
Center (18, -45) and radius=14sqrt5

need a solution for these :) thanks

Answer 1

Given lines are perpendicular because m₁ = 2, m₂ = - 1/2 and m_`1·m₂ = - 1. Center of circle is (x, 27 - 4x)

From this point distances to given lines equal: r = (2x - 27 + 4x - 11)/√5 = - (x + 54 - 8x + 2)/√5;

6x - 38 = 7x - 56; x = 18; y = 27 - 4x = 27 - 72 = - 45; (18, - 45) is center; r = (6·18 - 38)/√5 = 14√5