Slope Of Common Tangent To Parabolas y2 = 4x and x2 = 8y is

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.

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

The vertex of a parabola is the point (a, b) and latus-rectum is of length l. If the axis of the parabola is along the positive direction of y-axis. Then its equation is

If a focal chord with positive slope of the parabola y² = 16xtouches the circle x² + y² – 12x + 34 = 0, then m is