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
A.
Given that, the ordinate decreases at the same rate at which the abscissa increases, therefore we have
...(i)
Also, equation of ellipse
16x2 + 9y2 = 400 ...(ii)
On differentiating w.r.t. t, we get
Using Eq. (iii) in Eq. (ii), we get
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