A quadrilateral is inscribed in a parabola `y^2=4a x` and three of its sides pass through fixed points on the axis. Show that the fourth side also passes through a fixed point on the axis of the parabola.

From a variable point on the tangent at the vertex of a parabola y^2=4a x , a perpendicular is drawn to its chord of contact. Show that these variable perpendicular lines pass through a fixed point on the axis of the parabola.

The circle passing through the point (-1,0) and touching the y-axis at (0,2) also passes through the point:

The tangent to the curve y=xe^(x^2) passing through the point (1,e) also passes through the point

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

Aray of light passing through the point(1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5,3). Find the coordinates of A.

L O L ' and M O M ' are two chords of parabola y^2=4a x with vertex A passing through a point O on its axis. Prove that the radical axis of the circles described on L L ' and M M ' as diameters passes though the vertex of the parabola.

Find the locus of the midpoint of chords of the parabola y^2=4a x that pass through the point (3a ,a)dot

Let L be a normal to the parabola y^2=4xdot If L passes through the point (9, 6), then L is given by

Three straight lines mutually perpendicular to each other meet in a point P and one of them intersects the x-axis and another intersects the y-axis, while the third line passes through a fixed point(0,0,c) on the z-axis. Then the locus of P is