﻿ 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. : Kaysons Education

# 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.

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## Question

### Solution

Correct option is

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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