The abscissa of A and B are the roots of the equation x 2 + 2ax – b 2 = 0 and their ordinates are the roots of the equation y 2 + 2py – q 2 = 0. The equation of the circle with AB as diameter:
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Let A ≡ (x 1 , y 1 ) and B ≡ (x 2 , y 2 )
x 1 , x 2 are roots of x 2 + 2ax – b 2 = 0
⇒ (x – x 1 ) (x – x 2 ) = x 2 + 2ax – b 2
y 1 , y 2 are roots of y 2 + 2py – q 2 = 0
⇒ (y – y 1 ) (y – y 2 ) = y 2 + 2py – q 2
Now equation of circle with AB as diameter is
(x – x 1 ) (x – x 2 ) + (y – y 1 ) (y – y 2 ) = 0
⇒ x 2 + 2ax – b 2 + y 2 + 2py – q 2 = 0
⇒ x 2 + y 2 + 2ax + 2py – b 2 – q 2 = 0
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