The coordinates of a moving point P are `(2t^(2) + 4, 4t + 6) ` , show that the locus of P is a parabola.

The coordinates of a moving point p are (2t^(2) + 4, 4t+6) . Then its locus will be a

For all values of theta , the coordinates of a moving point P are (acostheta,asintheta) , the locus of P will be a-

For all values of theta , the coordinates of a moving point P are (acostheta,bsintheta) , find the equation to the locus of P.

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

The coordinates of moving point P are ((2t+1)/(3t-2),(t-1)/(t+1)) , where t is a variable parameter . Find the equation to the locus of P.

The coordinates of a moving point P are (ct+(c)/(t),ct-(c)/(T)) , where t is a variable parameter . Find the equation to the locus of P.

A(3, 0) and B(-3, 0) are two given points and P is a moving point : if bar(AP) = 2bar(BP) for all positions of P, show that the locus of P is a circle. Find the radius of the circle.

The coordinates of a moving point P are [6sectheta ,8tantheta] where theta is a variable parameter . Show that equation to the locus of P is (x^(2))/(36)-(y^(2))/(64)=1 .

Q is any point on the parabola y^(2) =4ax ,QN is the ordinate of Q and P is the mid-point of QN ,. Prove that the locus of p is a parabola whose latus rectum is one -fourth that of the given parabola.

PC is the normal at P to the parabola y^2=4ax, C being on the axis. CP is produced outwards to Q so that PQ =CP ; show that the locus of Q is a parabola.