﻿ The line joining the origin to the points of intersection of x2 + y2 + 2gx + c = 0 and x2 + y2 + 2fy – c = 0 are at right angles, if : Kaysons Education

# The Line Joining The Origin To The Points Of Intersection Of x2 + y2 + 2gx + c = 0 And x2 + y2 + 2fy – c = 0 Are At Right Angles, If

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## Question

### Solution

Correct option is

g2 – f2 = 2c

Equation of common chord is fy – gx = c, equation of the line joining the origin to the points of intersection of the circles is  x2 + y2 + 2g x

which are at right angle if

c + c – 2g2 + f2 + g2 = 0 ⇒ g2 – f2 = 2c

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