If P (at²₁,2at₁)and Q (at²₂,2at₂),are variable points on the curve y² = 4ax and PQ subtends a right angle at the vertex , than t₁t₂ =

The equation to the normal to the parabola y² = 4x at (1,2) is

Match the following

The locus of the poles of chords of the parabola y² = 4ax, which subtend a right angle at the vertex is

If the equation of the parabola whose axis is parallel to x – axis and passing through (2,-1) (6,1) (3, -2) is ay2 + bx + cy + d = 0 then the ascending order of a,b,c,d is

if the focus is (1,-1) and the directrix is the line x + 2y – 9 = 0, the vertex of the parabola is at

I : If the points (2,-1), (5,k) are conjugate with respect to the parabola x² = 8y then k = 7

II: If the lines 2x + 3y + 12 = 0,x – y + k = 0 are conjugate with respect to the parabola y² = 8x then k = -12

If the normal at (1,2) on the parabola again at the point (l2,2t), then the value of t is

If P is a point on the parabola y² = 4ax such that the subtangent and subnormal at P are equal, then the coridinate of P are

The tangents to the parabola y² = 4ax at p (t₁) and Q (t₂) intersect at R. the area of Δ PQR is