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Question

The locus of the mid point of a chord of the circle x2+y2=4 which subtends a right angle at the origin is

A
x+y=2
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B
x2+y2=1
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C
x2+y2=2
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D
x+y=1
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Solution

The correct option is B x2+y2=2
Given the equation of circle,

x2+y2=4

Let the centre of the circle be O(0,0)

and midpoint of the chord AB be N(x,y)

AOB=90° , since the chord subtends a right angle at origin.

NOB=902=45

Equation of circle is x2+y2=4

ONOB=x2+y22

12=x2+y22

By squaring both sides 12=x2+y24

x2+y2=2

894203_455316_ans_21e00d0e45bc4809a614936db1b13bdc.JPG

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