The Line x – Y + 2 = 0 Touches The Parabola y2 = 8x at The Point

The length of the subnormal to the parabola y² = 4ax at any point is equal to

The slope of the normal at the point (at², 2at) of parabola y² = 4ax  is

Equation of locus of a point whose distance from point (a, 0) is equal to its distance from y-axis is

Through the vertex O of parabola y² = 4x, chords OP and OQ are drawn at right angles to one another. The locus of the middle point of PQ is

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y² = 4ax is another parabola with directrix

The equation of common tangent to the curves y² = 8x and xy = –1 is

From the point (–1, 2) tangent lines are drawn to the parabola y² = 4x, then the equation of chord of contact is

For the above problem, the area of triangle formed by chord of contact and the tangents is given by

A point moves on the parabola y² = 4ax. Its distance from the focus is minimum for the following value(s) of x.

If t is the parameter for one end of a focal chord of the parabola y² = 4ax, then its length is