A Point Moves On The Parabola y2 = 4ax. Its Distance From The Focus Is Minimum For The Following Value(s) Of x.

The locus of a point whose some of the distance from the origin and the line x = 2 is 4 units, is

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

The line x – y + 2 = 0 touches the parabola y² = 8x at the point