The distance between the directrices of a rectangular hyperbola x2 - y2 = a2 is 10 units, then distance between its foci is
5
20
The equation of the tangents of hyperbola 3x2 - 4y2 = 12 which cuts equal intercepts from both the axes, are
4y - 3x = 0
Equation of the tangent to the hyperbola 2x2 - 3y2 = 6. Which is parallel to the line y - 3x - 4 = 0 is
y = 3x + 8
y = 3x - 8
y = 3x + 2
None of these
The equation of circle which touches the axes and the line and whose centre lies inthe first quadrant is x2 + y2 - 2cx - 2cy + c2 = 0. Then, c is equal to
1
2
3
6
The equation of the parabola having the focus at the point (3, - 1) and the vertex at (2, - 1)is
y2 - 4x - 2y + 9 = 0
y2 + 4x + 2y - 9 = 0
y2 - 4x + 2y + 9 = 0
y2 + 4x - 2y + 9 = 0
Find the equation of tangents to the ellipse which cut off equal intercepts on the axes.
None of the above
B.
The locus ofthe point of intersection of the lines and ( is a variable) will be
a circle
a staright line
a parabola
an ellipse
The locus of the mid points of the chords of a circle which subtend a right angle at its centre (equation ofthe circle is x2 + y2 = a2)will be
x2 + y2 = 3a2
x2 + y2 =
2(x2 + y2) = a2
4(x2 + y2) = a2
If the line 3x - 2y + p = 0 is normal to the circle x2 + y2 = 2x - 4y - 1, then p will be
- 5
7
- 7
5
If the two circles x2 + y2 = r2 and x2 + y2 - 10x + 16 = 0 intersect at two real points, then
1 < r < 7
3 < r < 10
2 < r < 9
2 < r < 8