﻿ Find the coordinates of the middle point of the chord which the circle x2+ y2 + 4x – 2y – 3 = 0 cut off the line x – y + 2 = 0.    : Kaysons Education

# Find The Coordinates Of The Middle Point Of The Chord Which The Circle x2+ y2 + 4x – 2y – 3 = 0 Cut Off The Line x – y + 2 = 0.

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## Question

### Solution

Correct option is

Centre and radius of the circle x2 + y2 + 4x – 2y – 3 = 0 are (–2, 1) and  respectively.

Draw perpendicular from O upon x – y + 2 = 0 is OM

Equation of OM which is perpendicular to x – y + 2 = 0 is x + y = λ, it passes through (–2, 1)

Then            –2 + 1 = λ

Then equation of OM in x + y + 1= 0

Since M is the midpoint of PQ which is point of intersection of

x – y + 2 = 0 and x + y +1 = 0, coordinates of M is

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