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Chord of Contact

The abscissas...

Question

The abscissas of two points $A$ and $B$ are the roots of the equation $x^{2} + 2 x - a^{2} = 0$ and their ordinates are the roots of the equation $y^{2} + 4 y - b^{2} = 0$ . Find the equation of the circle with $A B$ as diameter. Also find the co-ordinates of the centre and the length of the radius of the circle .

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Solution

$x^{2} + y^{2} + 2 x + 4 y - a^{2} - b^{2} = 0$
Centre $(- 1, - 2)$ and radius $\sqrt{a^{2} + b^{2} + 5}$

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