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
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
Two diameters with slopes m1,m2 are conjugate if
m1m2 = -1
m1m2 = - b2/a2
m1m2 = a2/b2
m1m2 = b2/a2
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 eccentricity of the hyperbola x2 - 4y2 = 1 is
√5/2
√3/2
2/√5
2/√3
Sum of the focal distance of an ellipse is equal to
2 b
2 a
2 ab
a + b
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)
If e ane e1 are the eccentricities of the hyperbolas xy = c2 and x2 - y2 = c2 , then e2 + e2 is equal to
1
4
6
8
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
