The abscissa of A and B are the roots of the equation x 2 + 2 a x - b 2 = 0 and their ordinates are the roots of the equation y 2 + 2 p y - q 2 = 0 . The equation of the circle with A B as diameter is

Step-by-step solution

Let, A ≡ x 1 , y 1 and B ≡ x 2 , y 2 x 1 , x 2 are roots of x 2 + 2 a x - b 2 = 0 ⇒ x - x 1 x - x 2 = x 2 + 2 a x - b 2 y 1 , y 2 are roots of y 2 + 2 p y - q 2 = 0 ⇒ y - y 1 y - y 2 = y 2 + 2 p y - q 2 Now, equation of circle with A B as diameter is x - x 1 x - x 2 + y - y 1 y - y 2 = 0 ⇒ x 2 + 2 a x - b 2 + y 2 + 2 p y - q 2 = 0 ⇒ x 2 + y 2 + 2 a x + 2 p y - b 2 - q 2 = 0