# if the coordinates of a variable point P be (cos theta + sin theta, sin theta - cos theta ), where theta is the parameter then the equation of locus of P is

Siva Sankar
19 Points
4 years ago
Given the gen.pt is $(cos\theta+sin\theta,sin\theta-cos\theta)$
This imply  $x=cos\theta+sin\theta$ and $y=sin\theta-cos\theta$.        Square both x and y and add them up.

$y^{^{2}}=1-2sin\theta*cos\theta$
$x^{^{2}}=1+2sin\theta*cos\theta$
This implies $x^{^{2}} + y^{^{^{2}}} =2.$
It is a circle with center(0,0) and radius root2  ​  ​