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
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
C.
Given that will lie on the circle (from the given figure). Since, point lies on the region containing origin.
So, point will be on the shaded region.
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