A to Z Exams

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 =

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

Match the following Parabola Focus y2 –x – 2y + 2 = 0 (1,2) y2 – 8x – 4y – 4 = 0 (-2,5) x2 + 4x – 8y + 28 = 0 (1,-1) x2 – 2x – 8y – 23 = 0 (5/4,1)

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

The point on the parabola y2 = 36x whose oridinate is three times its abscissa is

the equation of the parabola whose axis is parallel to x –axis and passing through (- 2,1), (1,2), (-1,3) is

The length of the latus rectum of the parabola x2 + 4x – 8y + 28 = 0 is

The equation of the axis of the parabola 3x2 – 9x + 5y -2 = 0 is

The sub-tangent, ordinate and sub-normal to the parabola y2 = 4ax at a point ( diffferent from the origin ) are in

The length of the chord intercepted bt the parabola y = x2 + 3x  on the line x + y = 5 is

The equation of the axis of the parabola (y + 3)2 = 4(x – 2) is

Two straight lines are perpendicular to each other. One of them touches the parabola y2 = 4a (x + a) and the other touches y2 = 4b (x + b). the locus of the point of intersectionof the two lines is

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

The equation of the axis of the parabola (y + 3)2 = 4(x – 2) is

The equation of the tangent to the parabola y2 = 12x at (3, -6) is