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Length of Intercept Made by a Circle on a Straight Line

The abscissae...

Question

The abscissae of A and B are the roots of the equation $x^{2} + 2 a x - b^{2} = 0$ and their coordinates are the roots of the equation $y^{2} + 2 p y - q^{2}$ = 0. The equation of the circle with AB as diameter

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Solution

The correct option is A

Let $A (x_{1}, y_{1})$ and $B (x_{2}, y_{2})$ , then

$x_{1} + x_{2} = - 2 a$ ,
$x_{1} x_{2} = - b^{2}$

$y_{1} + y_{2} = - 2 p$ ,
$y_{1} y_{2} = - q^{2}$
Equation of the circle with AB as diameter.
$(x - x_{1}) (x - x_{2}) + (y - y_{1}) (y - y_{2}) = r$
$x^{2} + y^{2} + 2 a x + 2 p y - b^{2} - q^{2} = 0$

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