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

If a chord of the parabola y^2 = 4ax touches the parabola y^2 = 4bx , then show that the tangent at the extremities of the chord meet on the parabola b^2 y^2 = 4a^2 x .

The line 4x+6y+9 =0 touches the parabola y^(2)=4ax at the point

The normals at the extremities of a chord PQ of the parabola y^2 = 4ax meet on the parabola, then locus of the middle point of PQ is

The locus of the middle points of the focal chords of the parabola, y 2 =4x

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

. A straight line touches the rectangular hyperbola 9x^2-9y^2=8 and the parabola y^2= 32x . An equation of the line is

The locus of the middle points of normal chords of the parabola y^2 = 4ax is-