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the variable line xcosa+ysina=2 cuts the x and y axes at A and B respectively.Find the locus of the vertex P of the rectangle OAPB,O being the origin.
Intercepts of x and y axes respectively are: 2seca and 2coseca.Let P(h,k) be the coordinates.then from rectangle property,h = 2/cosa and k = 2/sinaorcosa = 2/h and sina = 2/ksquaring and adding both ratios we get,1/h^2 + 1/k^2 = ¼Hence, the locus of P point is:1/x^2 + 1/y^2 = ¼.
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