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Question

Locus of image of the point P(h,k) with respect to the line mirror which passes through the origin is

A
x2+y2=hx+ky
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B
x2+y2=h2+k2
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C
x2+y2=h2+hx
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D
x2+y2=h2+k2+hx+ky
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Solution

The correct option is B x2+y2=h2+k2
Let the line be y=mx and image of P(h,k) be Q(a,b)
Then mid-point of PQ will lie on y=mx
(h+a2)m=b+k2
m=b+kh+a

Also, line PQ is perpendicular to line y=mx
(b+kh+a)(bkah)=1b2k2=h2a2a2+b2=h2+k2

Hence locus will be x2+y2=h2+k2

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