The abscissa of two points A and B are the roots of the equation x2 + 2ax – b2 = 0 and their ordinates are the roots of the equation x2 + 2px –q2 = 0. Find the equation and the radius of the circle with AB as diameter.
Given equations are
x2 + 2ax – b2 = 0 …(1)
and x2 + 2px – q2 = 0 …(2)
Let the roots of the equation (1) be α and β and those of equation (2) by γ and δ. Then
Let A ≡ (α, γ) and B ≡ (β, δ).
Now equation of circle whose diameter is AB will be
(x – α) (x – β) + (y – γ) (γ – δ) = 0
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