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

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

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

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