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.

From the point where any normal to the parabola y^2 = 4ax meets the axis, is drawn a line perpendicular to this normal, prove that this normal always touches an equal parabola y^2 +4a(x-2a)=0 .

If the line y=mx+c is a normal to the parabola y^2=4ax , then c is

The line lx+my+n=0 is a normal to the parabola y^2 = 4ax if

Find the point where the line x+y=6 is a normal to the parabola y^2=8x .

Equation of normal to parabola y^2 = 4ax at (at^2, 2at) is

Equation of normal to parabola y^2 = 4ax at (at^2, 2at) is

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

Length of the shortest normal chord of the parabola y^2=4ax is

The length of the subnormal to the parabola y^(2)=4ax at any point is equal to

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.