`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 (a) parabola (b) hyperbola (c) circle (d) none of these

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 a/n parabola (b) hyperbola hyperbola (d) circle

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

A tangent to the parabola x^2 =4ay meets the hyperbola xy = c^2 in two points P and Q. Then the midpoint of PQ lies on (A) a parabola (C) a hyperbola (B) an ellipse (D) a circle

A tangent to the parabola y^2 + 4bx = 0 meets the parabola y^2 = 4ax in P and Q. The locus of the middle points of PQ is:

Parabola y^2=4a(x-c_1) and x^2=4a(y-c_2) , where c_1a n dc_2 are variable, are such that they touch each other. The locus of their point of contact is (a) x y=2a^2 (b) x y=4a^2 (c) x y=a^2 (d) none of these

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

The tangent at the point P(x_1, y_1) to the parabola y^2 = 4 a x meets the parabola y^2 = 4 a (x + b) at Q and R. the coordinates of the mid-point of QR are

A variable tangent to the parabola y^(2)=4ax meets the parabola y^(2)=-4ax P and Q. The locus of the mid-point of PQ, is

The ordinates of points P and Q on the parabola y^2=12x are in the ration 1:2 . Find the locus of the point of intersection of the normals to the parabola at P and Q.

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)