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` .

Chords of the circle x^(2)+y^(2)=a^(2) toches the hyperbola x^(2)/a^(2)-y^(2)//b^(2)=1 . Prove that locus of their middle point is the curve (x^2 +y^2)^2=a^(2)x^(2)-b^(2)y^(2)

Chords of the circle x^(2)+y^(2)=4 , touch the hyperbola (x^(2))/(4)-(y^(2))/(16)=1 .The locus of their middle-points is the curve (x^(2)+y^(2))^(2)=lambdax^(2)-16y^(2) , then the value of lambda is

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

If the circle x^(2)+y^(2)+2ax=0, a in R touches the parabola y^(2)=4x , them

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.