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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.

Grade:12th pass

1 Answers

Vikas TU
14149 Points
6 years ago
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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