Question

 Lines 5x + 12y –10 = 0 and 5x – 12y – 40 = 0 touch a circle C₁ (of diameter 6). If centre of C₁ lies in the first quadrant, find concentric circle C₂ which cuts intercepts of length 8 units on each given line. 

Answer 1

Consider centre of required circle is (h, k) and by using perpendicular distance formula from centre to given tangent we will get value of h and k

Let centre of circle C₁ be O (h, k), where h > 0 and k > 0 

WP = 4 and OP = 3 … (given)

⇒ k = 2 (as k > 0)

Hence, equation of required circle is 

(x – 5)² + (y – 2)² = 25