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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

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

Grade:11

1 Answers

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  ​  ​
 
 
 
 

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