Let circle C₁ be given by the equation x^2 + y^2 - 10x - 16y + 85 = 0 . It is reflected across a line L to form circle C₂ . Let A be the rightmost point on C₂ . If point B(0, 3 ) lies on C₂ such that the length of the minor arc AB is (1/6)^ th of the perimeter of C₂ , and the y -coordinate of B is strictly greater than the y -coordinate of A , then if the equation of the line L is written in the form 3x + 4y = c , th

Step-by-step solution

The equation of circle C₁ can be written as (x-5)^2 + (y-8)^2 = 4 . Thus, the centre of C₁ is (5, 8) and its radius is r = 2 . Since C₂ is the reflection of C₁ , it also has a radius of r = 2 . Let its centre be (h, k) . Point A is the rightmost point on C₂ , so its parametric angle is 0 . Thus, A = (h+2, k) . The length of the minor arc AB is (1/6)^ th of the perimeter of C₂ , which means the angle subtended by arc AB at the centre is 1 6 2 = 3 . Since the y -coordinate of B is greater than that of A , the paramet