The length of the focal chord of the parbola y² = 4ax which makes an angle θ with its axis is

L and L’are ends of the latus rectum of the parabola x² = 6y. the equation of OL and OL’ where O is the origin is

The angle subtended at the focus by the normal chord of a parabola y²= 4ax at a point whose ordinate equal to abscisa is

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