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.

Question

Vikas TU · Answer

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/sina or cosa = 2/h and sina = 2/k squaring and adding both ratios we get, 1/h^2 + 1/k^2 = ¼ Hence, the locus of P point is: 1/x^2 + 1/y^2 = ¼.

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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.

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.

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