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
C.
3
Let S1 = 3x2 + 5y2 - 32
and S2 = 25x2 + 9y2 - 450
At point (3, 5)
S1 = 3(3)2 + 5(5)2 - 32 = 120 > 0
and S2 = 25(3)2 + 9(5)2 - 450
= 225 + 225 - 450 = 0
Thus, Point (3, 5) lies outside the first ellipse and for second ellipse lies on the ellipse.
Hence, two tangents for first ellipse and one tangent for second ellipse can be drawn.
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)
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