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LOL' and MOM' are two chord of parabola ...

LOL' and MOM' are two chord of parabola `y^(2)=4ax` with vertex A passing through a point O on its axis. Prove that the radical axis of the circles described on LL' and MM' as diameters passes though the vertex of the parabola.

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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.

Show that the locus of the middle points of chords of the parabola y^(2) = 4ax passing through the vertex is the parabola y^(2)= 2ax .

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

Show that the locus of the middle points of chords of the parabola y^(2) = 4ax passing through the vertex is the parabola y^(2) = 2ax

The parabola y^2=4ax passes through the point (2,-6). Find the length of the latus rectum.

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.

Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

If two intersecting chords of a circle make equal angles with diameter passing through their point of intersection, prove that the chords are equal.

Length of the focal chord of the parabola y^2=4ax at a distance p from the vertex is:

If the normal chord of the parabola y^(2)=4x makes an angle 45^(@) with the axis of the parabola, then its length, is

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