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

If the points (2,4), (k,6) are conjugate with respect to the parabola y² = 4x then k =

If (9,12) is one end of a double oridinate of the parabola y² = 16x, then its equation is

the equation of the parabola whose axis is parallel to y –axis and passing through  is (-3,1), (1,1) is

If 2x + y + a = 0 is a focal chord of the parbola y² + 8x = 0

The locus of the point of intersection of two tangents to the parabola y² = 4ax which make the θ₁ and θ₂ with the axis so that tan θ₁ tanθ₂  = k is