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Question

The locus of the mid points of the chord of the circle x2+y2=4, which subtended a right angle at the origin is

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

The correct option is B x2+y2=2
Let (h,k) be the mid-point of a chord of circle x2+y2=4.

Therefore, the equation of chord-

hx+ky4=h2+k24

hx+ky=h2+k2.....(1)

Equation of straight line joining the origin to the points of intersection of

(1) and the circle x2+y24-

x2+y2=4(hx+kyh2+k2)2.....(2)

Since the above pair of lines subtends a the right angle.

(h2+k2)=42h2+k2=2

Hence the locus of the mid-point of the chord is x2+y2=2.

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