The normals at P,Q,R on the parabola `y^2=4ax` meet in a point on the line y=c. Prove that the sides of the `DeltaPQR` touch the parabols `x^2=2cy`.

The normals at P, Q, R on the parabola y^2 = 4ax meet in a point on the line y = c. Prove that the sides of the triangle PQR touch the parabola x^2 = 2cy.

IF three distinct normals to the parabola y^(2)-2y=4x-9 meet at point (h,k), then prove that hgt4 .

If the normals at P, Q, R of the parabola y^2=4ax meet in O and S be its focus, then prove that .SP . SQ . SR = a . (SO)^2 .

The normal to parabola y^(2) =4ax from the point (5a, -2a) are

Normals at points P, Q and R of the parabola y^(2)=4ax meet in a point. Find the equation of line on which centroid of the triangle PQR lies.

From the point where any normal to the parabola y^2 = 4ax meets the axis, is drawn a line perpendicular to the normal. Prove that the line always touches an equal parabola.

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

Consider the parabola y^(2)=8x, if the normal at a point P on the parabola meets it again at a point Q, then the least distance of Q from the tangent at the vertex of the parabola is

Consider the parabola y^(2)=8x, if the normal at a point P on the parabola meets it again at a point Q, then the least distance of Q from the tangent at the vertex of the parabola is

The normal to the parabola y^(2)=8ax at the point (2, 4) meets the parabola again at the point