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
A.
1
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
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