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 number of common tangents to the circles x2 + y2 = 4 and x2 + y2 - 6x - 8y = 24 is
0
1
3
4
B.
1
The centres of the given circles x2 + y2 = 4 and x2 + y2 - 6x - 8y = 24 are C1(0, 0) and C2(3, 4) respectively. Their radii are r1 = 2 and r2 = 7 respectively.
We have, C1C2 = 5 < sum of radii
But C1C2 = difference of radii
Thus, the given circles touch each other internally.
Hence, the number of common tangent is only one.
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
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