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
C.
Let the eccentric angle ofthe point be 0, then 1ts coordinates are .
Centre of a given ellipse is (0, 0).
According to the question,
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
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