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The locus of the middle point of chords of the circle $x^{2} + y^{2} = a^{2}$ which pass through the fixed point $(h, k),$ is

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x2+y2−hx−ky=0

x2+y2+hx+ky=0

x2+y2−2hx−2ky=0

x2+y2+2hx+2ky=0

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detailed solution

Correct option is A

Let (α, β) be the mid point of a chord of the circle x2+y2=a2. Then its equation is αx+βy=α2+β2 [Using S=T]This passes through (h, k).∴ αh+βk=α2+β2Hence, the locus of (α, β) isx2+y2=hx+ky⇒x2+y2−hx−ky=0.

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The locus of the middle point of chords of the circle x2+y2=a2 which pass through the fixed point (h, k), is

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The locus of the middle point of chords of the circle $x^{2} + y^{2} = a^{2}$ which pass through the fixed point $(h, k),$ is