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Locus of mid point of the portion between the axes o $x \cos α + y \sin α = p$ where $p$ is constant is

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x2+y2=4/p2

x2+y2=4p2

1/x2+1/y2=2/p2

1/x2+1/y2=4/p2

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detailed solution

Correct option is D

If (h,k) is the mid-point, thenh=p/2cos⁡α,k=p/2sin⁡αso (p/2h)2+(p/2k)2=cos2⁡α+sin2⁡α=1⇒ 1/h2+1/k2=4/p2Locus of ( h ,k ) is 1/x2+1/y2=4/p2

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Locus of mid point of the portion between the axes o xcos⁡α+ysin⁡α=p where p is constant is

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Locus of mid point of the portion between the axes o $x \cos α + y \sin α = p$ where $p$ is constant is