If tangent at `P` and `Q` to the parabola `y^2 = 4ax` intersect at `R` then prove that mid point the parabola, where `M` is the mid point of `P` and `Q.`

If the normals at two points P and Q of a parabola y^2 = 4x intersect at a third point R on the parabola y^2 = 4x , then the product of the ordinates of P and Q is equal to

If the tangents at the points P and Q on the parabola y^2 = 4ax meet at R and S is its focus, prove that SR^2 = SP.SQ .

If any tangent to the parabola x^(2) = 4y intersects the hyperbola xy = 2 at two points P and Q, then the mid point of line segment PQ lies on a parabola with axis along:

A tangent to the parabola y^(2)=4ax meets axes at A and B .Then the locus of mid-point of line AB is

If the tangents at the points P and Q on the parabola y^(2)=4ax meet at T, and S is its focus,the prove that ST,ST, and SQ are in GP.

If any tangent to the parabola x^(2)=4y intersects the hyperbola xy=2 at two points P and Q , then the mid point of the line segment PQ lies on a parabola with axs along