If the coordinates of a variable point `P` are `(acostheta,bsintheta),` where `theta` is a variable quantity, then find the locus of `Pdot`

If the coordinates of a variable point P be (a cos theta, b sin theta) , where theta is a variable quantity, find the locus of P .

If the coordinates of a variable point P be (cos theta + sin theta, sin theta - cos theta) , where theta is a variable quantity, find the locus of P .

If the coordinates of a variable point P be (t+ 1/t , t- 1/t) , where t is a variable quantity, then find the locus of P .

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

If the coordinates of a vartiable point P be (t+(1)/(t), t-(1)/(t)) , where t is the variable quantity, then the locus of P is

Vertices of a variable triangle are (3,4);(5cos theta,5sin theta) and (5sin theta,-5cos theta) where theta is a parameter then the locus of its circumcentre is

The coordinates of a moving point P are (at^(2),2at), whereis a variable parameter.Find the equation to the locus of P.

If x=acostheta , y=bsintheta then eliminate theta .