For different values of a, the locus of the point of intersection of the two straight lines and
a hyperbola with eccentricity 2
an ellipse with eccentricity
a hyperbola with eccentricity
an ellipse with eccentricity
The circles x2 + y2 - 10x + 16 = 0 and x2 + y2 = a2 intersect at two distinct points, if
a < 2
2 < a < 8
a > 8
a = 2
For the two circles x2 + y2 = 16 and x2 + y2 - 2y = 0 there is/are
one pair of common tangents
only one common tangent
three common tangents
no common tangent
The equation of the tangent to the conic x2 - y2 - 8x + 2y + 11 = 0 at (2, 1) is
x + 2 = 0
2x + 1 = 0
x + y + 1 = 0
x - 2 = 0
The total number of tangents through the point ( 3, 5) that can be drawn to the ellipses 3x2 + 5y2 = 32 and 25x + 9y2 = 450 is
0
2
3
4
The equation of chord of the circle x2 + y2 - 4x = 0, whose mid-point is (1, 0) is
y = 2
y = 1
x = 2
x = 1
The coordinates of the focus of the parabola described parametrically by x = 5t2 + 2, y = 10t + 4 are
(7, 4)
(3, 4)
(3, - 4)
(- 7, 4)
The angle between the lines joining the foci of an ellipse to one particular extremity of the minor axis is 90°. The eccentricity of the ellipse is
1/8
1/√3
√(2/3)
√(1/2)
D.
√(1/2)
If the rate of increase of the radius of a circle is 5 cm/ s, then the rate of increase of its area, when the radius is 20 cm, will be
10
20
200
400