If chords of the hyperbola `x^(2)-y^(2)=a^(2)` touch the parabola `y^(2)=4ax` ,then mid-points of these chords lie on which of the following curves

Chords of the hyperbola,x^(2)-y^(2)=a^(2) touch the parabola,y^(2)=4ax. Prove that the locus of their middlepoints is the curve,y^(2)(x-a)=x^(3)

if the line 4x+3y+1=0 meets the parabola y^(2)=8x then the mid point of the chord is

The locus of the mid-point of the chords of the hyperbola x^(2)-y^(2)=4 , that touches the parabola y^(2)=8x is

If a normal of slope m to the parabola y^(2)=4ax touches the hyperbola x^(2)-y^(2)=a^(2), then

A variable chord of the parabola y^(2)=8x touches the parabola y^(2)=2x. The the locus of the point of intersection of the tangent at the end of the chord is a parabola.Find its latus rectum.

If x-2y-a=0 is a chord of the parabola y^(2)=4ax , then its langth, is