If (-3, 2) lies on the circle x2 + y2 + 2gx + 2fy + c = 0, which is concentric with the circle x2 + y2 + 6x + By - 5 = 0, then c is equal to
11
- 11
24
100
The eccentricity of the ellipse, which meets the straight line on the axis of x and the staraight line on the axis of y and whose axes lie along the axes of coordinate, is
None of the above
If and x2 - y2 = c2 cut at right angles, then
a2 + b2 = 2c2
b2 - a2 = 2c2
a2 - b2 = 2c2
a2b2 = 2c2
The equation of the conic with focus at (1, - 1) directrix along x - y + 1 = 0 and with eccentricity , is
x2 - y2 = 1
xy = 1
2xy - 4x + 4y + 1 = 0
2xy + 4x - 4y - 1 = 0
The locus of the mid-points of the focal chord of the parabola y2 = 4ax is
y2 = a(x - a)
y2 = 2a(x - a)
y2 = 4a(x - a)
None of these
A rod of length l slides with its ends on two perpendicular lines. Then, the locus of its mid point is
None of these
A.
Let both of the ends of the rod are on x-axis and y-axis. Let AB be rod oflength I and coordinates of A and B be (a, 0) and (0, b) respectively.
Let P (h, k) be the mid point of the rod AB.
Then,
The line joining (5, 0) to () is divided internally in the ratio 2 : 3 at P. If 0 varies, then the locus of P is
a straight line
a pair of straight lines
a circle
None of the above
If the equation of an ellipse is 3x2 + 2y2 + 6x - 8y + 5 = 0, then which of the following are true?
e =
centre is (- 1, 2)
foci are (- 1, 1) are (- 1, 3)
All of the above