Two rods of lengths a and b slides along the x-axis and y-axis respectively in such a manner that their ends are concyclic. The locus of the centre of the circle passing through the end points is
A
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B
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C
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D
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Solution
The correct option is C Let C(h, k) be the centre of the circle passing through the end points of the rod AB and PQ of lengths a and b respectively. CL and CM be perpendicular from C on AB and PQ respectively. Then AL=(12)AB=a2 PM=(12)PQ=b2 and CA=CP (radii of the same circle) ⇒k2+a24=h2+a24⇒4(h2−k2)=a2−b2 ∴The locus of (h, k) is 4(x2−y2)=a2−b2