The equation of the common tangent to the parabolas y2 = 2x and x2 = 16y will be
x + y + 2 = 0
x - 3y + 1 = 0
x + 2y - 2 = 0
x + 2y + 2 = 0
The equation of the tangent to the parabola y2 = 8x, which is parallel to the line 2x - y + 7 = 0, will be
y = x + 1
y = 2x + 1
y = 3x + 1
y = 4x + 1
The distance of a point on ellipse from its centre is 2. The eccentric angle of the point will be
None of these
The distance between the foci of a hyperbola is 16 and its eccentncity is . Its equation will be
x2 - y2 = 1
x2 - y2 = 20
x2 - y2 = 4
x2 - y2 = 32
Equation of the circle which passes through the origin and cuts intercepts of lengths a and b on axes is
x2 + y2 + ax + by = 0
x2 + y2 + ax - by = 0
x2 + y2 + bx + ay = 0
None of the above
If focus ofa parabolais at (3, 3) and its directrix is 3x - 4y = 2, then its latusrectum is
2
3
4
5
If the straight line y = 4x + c is a tangent to the ellipse , then c will be equal to
D.
The distance between the foci of a hyperbola is 16 and its eccentricity is - 2. Its equation will be
x2 - y2 = 32
y2 - x2 = 32
x2 - y2 = 16
y2 - x2 = 16
The number of common tangents that can be drawn to the circles x2 + y2 - 4x - 6y - 3 = 0 and x2 + y2 + 2x + 2y + 1 = 0 is
1
2
3
4
If two circles (x - 1)2 + (y - 3)2 = r2 and x2 + y2 - 8x + 2y + 8 = 0 intersect in two distinct points, then
2 < r < 8
r < 2
r = 2
r > 2