The locus of the point of intersection of two tangents to the parabola y² = 4ax which intercept a constant length d on the directrix is

The equation of the parabola whose axis is parallel to y –axis and passing through (4, 5) (-2, 11), (-4, 21) is

The normal at P cuts the axis of the parabola y² = 4ax in G and S is the focus of the parabola.If Δ SPG is equilateral then each side is of length

The vertex of a parabola is the point (a,b) and latusrectum is of length 1. If the axis of the parabola is along the positive direction of y – axis, then its equation is

The pole of the line 2x + 3y – 4 = 0 with respect to the parabola y² = 4x is

The locus of the point of intersection of two tangents to the parabola y² = 4ax which make an angle 30⁰ with one another is

A box contains 10 mangoes out of which 4 are rotten. Two mangoes are taken out together. If one of them is found to be good, the probability that the other is also good is

The locus of the point  of intersection of tangents to the parabola y² = 4(x + 1) and y2 = 8(x+2) which are perpendicular to each other is

The focus of a parabola is (2,3) and the foot of the perpendicular from the focus to the directrix is (4,5). The equation to the parabola is

The locus of the midpoint of the chords of the parabola y²= 6x which touch the circle x² + y² + 4x – 12 = 0 is