Show that the locus of points such that two of the three normals drawn from them to the parabola `y^2 = 4ax` coincide is `27ay^2 = 4(x-2a)^3`.

Three normals drawn from a point (h k) to parabola y^2 = 4ax

The locus of point of intersection of two normals drawn to the parabola y^2 = 4ax which are at right angles is

The locus of a point P(h, k) such that the slopes of three normals drawn to the parabola y^2=4ax from P be connected by the relation tan^(- 1)m_1^2+tan^(- 1)m_2^2+tan^(- 1)m_3^2=alpha is

The common tangent to the parabola y^2=4ax and x^2=4ay is

Prove that the locus of point of intersection of two perpendicular normals to the parabola y^(2) = 4ax isl the parabola y^(2) = a(x-3a)

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

The locus of foot of the perpendiculars drawn from the focus on a variable tangent to the parabola y^2 = 4ax is

The algebraic sum of the ordinates of the feet of 3 normals drawn to the parabola y^2=4ax from a given point is 0.

The locus of the point of intersection of the perpendicular tangents to the parabola x^2=4ay is .

The locus of foot of the perpendiculars drawn from the vertex on a variable tangent to the parabola y^2 = 4ax is