A. X2 + 8y + 12y2 + 10x + 24y + 9 = 0
B. 2x2 + 3xy -22y2 + 15x + 4y + 9 = 0
C. 3x2 + 18xy + 22y2 + 50x +64y + 19 = 0
D. X2 – 8y – 12y2 – 10x – 24y + 9 = 0
If z = log (tan x + tan y), then (sin 2x)∂z /∂x+(sin 2y) ∂z /∂y is equal to
The line y = x√2 + λ is a normal to the parabola y2 = 4ax, then λ =
The point on the parabola y = x2 + 7x + 2 closest to the line y = 3x – 3 is
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 =