If the vertex of the conic y - 4y = 4x - 4a always lies between the straight lines x + y = 3 and 2x + 2y - 1 = 0, then
2 < a < 4
0 < a < 2
The locus of the mid-points of chords of the circle x2 + y2 = 1, which subtends a right angle at the origin, is
x2 + y2 =
xy = 0
x2 - y2 = 0
x = - a
x = a
x = 0
x = -
C.
x = 0
Let P(at2, 2at) be a moving point on the parabola y2 = 4ax and S(a,0) be its focus. Let Q(h, k) be the mid-point of SP.
Then, h =
and k =
and t =
Thus, the locus of (h,k) is y2 = 2ax - a2
Now, y2 = 2ax - a2
The equation of the directrix of this parabola is
i.e. x = 0
The points of the ellipse 16x2 + 9y2 = 400 at which the ordinate decreases at the same rate at which the abscissa increases is/are given by
If the parabola x2 = ay makes an intercept of length units on the line y - 2x = 1, then a is equal to
1
- 2
- 1
2
If the point lies in the region between the lines x + y = 2 and x - y = 2 containing the origin, then 0 lies in
If the straight line (a - 1)x - by + 4 = 0 is normal to the hyperbola xy = 1, then which of the following does not hold?
a > 1, b > 0
a > 1, b < 0
a < 1, b < 0
a < 1, b > 0
If y = 4x + 3 is parallel to a tangent to the parabola y2 = 12x, then its distance from the normal parallel to the given line is
Let the equation of an ellipse be . Then, the radius of the circle with centre (0, ) and passing through the foci of the ellipse is
9
7
11
5