If a triangle is formed by any three tangents of the parabola `y^2 =4ax`, two of whose vertices lie on the parabola `x^2=4by`, then find the locus of the third vertex

If the chord of contact of tangents from a point P to the parabola y^(2)=4ax touches the parabola x^(2)=4by, then find the locus of P.

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

Assertion (A) : Orthocentre of the triangle formed by any three tangents to the parabola lies on the directrix of the parabola Reason ® : The orthocentre of the triangle formed by the tangents at t_1, t_2 ,t_3 to the parabola y^(2) =4ax is (-a ( t_1+t_2+t_3+t_1t_2t_3) )

An equilateral triangle is inscribed in the parabola y^2=4ax whose vertex is at of the parabola. Find the length of its side.

An equilateral triangle is inscribed in the parabola y^(2)=4ax whose vertex is at of the parabola.Find the length of its side.

A variable tangent to the parabola y^(2)=4ax meets the parabola y^(2)=-4ax P and Q. The locus of the mid-point of PQ, is

A variable tangent to the parabola y^(2)=4ax meets the parabola y^(2)=-4ax P and Q. The locus of the mid-point of PQ, is