The locus of the midpoint of the portion of the line xcosα+ysinα=p intercepted between the axes is

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x−2+y−2=4p−2

x2+y2=p2

x – y = p

x2+y−2=p2

answer is A.

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Detailed Solution

given line is xcosα+ysinα=p xcosαp+ysinαp=1 xpcosα+ypsinα=1A=(pcosα,0) B=(0,psinα) Let the point be ∴(h,k)=(p2cosα,p2sinα) ∴p24h2+p24k2=1Locus is 1x2+1y2=4p2

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