If the lines 2x + 3y + 12 = 0,x – y + 4k = 0 are conjugate with respect to the parabola y² = 8x then k =

I .thev locusv of the midpoints of chords of the parabola y² = 4ax which substends a right angle at the vertex is y2 = 2a (x – 4a)

II. the locus of midpoint of chords of the parabola y2 = 4ax which touch the circle X² + y² = a² is (y²- 2ax)2 = a2 (y² + 4a²)

The equation of the common tangent to x²+ y² = 8 and y² = 16x is

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