﻿ Find the co-ordinates of the middle point of the chord which the circlex2 + y2 + 4x – 2y – 3 = 0 cuts off the line x – y + 2 = 0. : Kaysons Education

# Find The Co-ordinates Of The Middle Point Of The Chord Which The Circlex2 + y2 + 4x – 2y – 3 = 0 Cuts Off The Line x – y + 2 = 0.

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## Question

### Solution

Correct option is

λ = –1

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

∴                      λ = –1.

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