The eccentricity of the hyperbola x2 - 4y2 = 1 is
√5/2
√3/2
2/√5
2/√3
The length of the latus rectum of the hyperbola is
2a2/b
2b2/a
b2/a
a2/b
If e,e' be the eccentricities of two conics S and S' and if e2 + e'2 = 3, then both S and S' can be
Ellipses
Parabola
Hyperbolas
None of these
The line y = 4x + c touches the hyperbola x2 - y2 = 1 iff
c = 0
c = ± √2
c = ± √15
c = ± √17
The equation x = a cos θ, y = b sin θ, 0 ≤ θ < 2 π, a ≠ b, represent
an ellipse
a parabola
a circle
a hyperbola
The equation ax2 + 2 hxy + by2 + 2 gx + 2 fy + c = 0 represents an ellipse if
Δ =0, h2 < ab
Δ ≠ 0, h2 < ab
Δ ≠ 0, h2 > ab
Δ ≠ 0, h2 = ab
The diameter of 16x2 - 9y2 = 144 which is conjugate to x = 2y is
y = 16/9 x
y = 32/9 x
x = 16/9 y
x = 32/9 y
A rectangular hyperbola is one in which
the two axes are rectangular
the two axes are equal
the asymptotes are perpendicular
the two branches are perpendicular
For the ellipse , the foci are
(± 1, 0)
(0, ± 1)
(± 1/√2, 0)
(± 1/2 , 0)
The latus rectum of the ellipse 5x2 + 9y2 = 45 is
10/3
5/3
5√5/3
10√5/3
