`P(x , y)` is a variable point on the parabola `y^2=4a x` and `Q(x+c ,y+c)` is another variable point, where `c` is a constant. The locus of the midpoint of `P Q` is

let P be the point (1, 0) and Q be a point on the locus y^2= 8x . The locus of the midpoint of PQ is

Let P be the point (1,0) and Q be a point on the locus y^(2)=8x . The locus of the midpoint of PQ is

Parabola y^2=4a(x-c_1) and x^2=4a(y-c_2) where c_1 and c_2 are variables, touch each other. Locus of their point of contact is

P,Q and R three points on the parabola y^(2)=4ax . If Pq passes through the focus and PR is perpendicular to the axis of the parabola, show that the locus of the mid point of QR is y^(2)=2a(x+a) .

The locus of the midpoint of the focal distance of a variable point moving on theparabola y^2=4a x is a parabola whose (a)latus rectum is half the latus rectum of the original parabola (b)vertex is (a/2,0) (c)directrix is y-axis. (d)focus has coordinates (a, 0)

A point P(x , y) moves in the xy-plane such that x=acos^2theta and y=2asintheta, where theta is a parameter. The locus of the point P is a/an

Let P be the midpoint of a chord joining the vertex of the parabola y^(2) = 8x to another point on it . Then locus of P .

The triangle P Q R of area A is inscribed in the parabola y^2=4a x such that the vertex P lies at the vertex of the parabola and the base Q R is a focal chord. The modulus of the difference of the ordinates of the points Qa n dR is

Let P be a variable point on a circle C and Q be a fixed point outside C. If R is the midpoint of the line segment PQ, then locus of R is

If P is any point on the plane l x+m y+n z=pa n dQ is a point on the line O P such that O P.O Q=p^2 , then find the locus of the point Qdot