If Normal At The Point (at2, 2at) In The Parabola y2 = 4axintersects The Parabola Again At The (am2, 2am), Then Find The Minimum Value Of m2.

The vertex of the parabola y² = 8x is at the center of a circle and the parabola cuts the circle at the ends of its latus rectum. Then the equation of the circle is

Find the equation of the parabola whose focus is (1, 1) and the directrix is x + y + 1 = 0.

If the line 2x + 3y = 1 touch the parabola y² = 4ax at the pointP. Find the focal distance of the point P.

Find the angle between the tangents of the parabola y² = 8x, which are drawn from the point (2, 5).

Find the locus of middle point of chord y² = 4ax drawn through vertex.

Find the locus of the mid-point of the chords of the parabola y² = 4ax which subtend a right angle at the vertex of the parabola.

Show that the normal at a point (at², 2at) on the parabola y² = 2ax cuts the curve again at the point whose parameter .

Show that the normal at a point (at², 2at) on the parabola y² = 2ax cuts the curve again at the point whose parameter .

Find the locus of a pint P which moves such that two of the three normal’s drawn from it to the parabola y² = 4ax are mutually perpendicular.

The equation of circle touching the parabola y² = 4x at the point  (1, –2) and passing through origin is