The normal at (a, 2a) on y2 = 4ax, meets the curve again at (at, 2at ), then the value of t is
- 1
1
- 3
3
If a set A contains n elements, then which of the following. cannot be the number of reflexive relations on the set A?
2n + 1
2n - 1
2n
The relation on the set A = {x : } is defined by R = {(x, y) : y = } Then, the number of elements in the power set of R is
8
16
32
64
The combined equation of the asymptotes of the hyperbola 2x2 + 5xy + 2y2 + 4x + 5y = 0 is
2x2 + 5xy + 2y2 + 4x + 5y - 2 = 0
2x2 + 5xy + 2y2 = 0
2x2 + 5xy + 2y2 + 4x + 5y + 2 = 0
None of the above
C.
2x2 + 5xy + 2y2 + 4x + 5y + 2 = 0
Let the equation of asymptotes be,
2x2 + 5xy + 2y2 + 4x + 5y + = 0 ...(i)
The above equation represents a pair of straight lines.
Therefore, abc + 2fgh - af2 - bg2 - ch2 = 0
Here, a = 2, b = 2,
and c = ,
On putting the value of in Eq. (i), we get
2x2 + 5xy + 2y2 + 4x + 5y + 2 = 0
which is the equation of the asymptotes.
A point on the ellipse : at a distance equal to the mean of length of the semi-major and semi-minor axes from the centre, is
The parametric coordinates of any point on the parabola whose focus is (0, 1) and the directrix is x + 2 = 0, are
(t2 - 1, 2t + 1)
(t2 + 1, 2t + 1)
(t2, 2t)
(t2 + 1, 2t - 1)