Show that the locus of the poles w.r.t. the parabola `y^2 = 4ax` of tangents to `x^2 - y^2 = a^2` is the ellipse `4x^2 + y^2 = 4a^2`.

Prove that the locus of the poles of tangents to the parabola y^2=4ax with respect to the circle x^2+y^2=2ax is the circle x^2+y^2=ax .

A tangent to the ellipse x^2+4y^2=4 meets the ellipse x^2+2y^2=6 at P&Q.

Find the locus of the midpoint of normal chord of parabola y^2=4ax

The locus of the poles of tangents to the parabola y^(2)=4ax with respect to the parabola y^(2)=4ax is

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

Prove that the locus of the middle points of all chords of the parabola y^2 = 4ax passing through the vertex is the parabola y^2 = 2ax .

The locus of the midpoints of the focal chords of the parabola y^(2)=4ax is

The equation of the common tangent to the parabolas y^2= 4ax and x^2= 4by is given by

Show that the locus of point of intersection of perpendicular tangents to the parabola y^2=4ax is the directrix x+a=0.

Find the position of points P(1,3) w.r.t. parabolas y^(2)=4x and x^(2)=8y .