The equation of a directrix of the ellipse is
y = 25/3
x = 3
x = -3
x = 3/25
The equation represents
an ellipse
a parabola
a hyperbola
a circle
The line y = 4x + c touches the hyperbola x2 - y2 = 1 iff
c = 0
c = ± √2
c = ± √15
c = ± √17
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 locus of the points of intersection of perpendicular tangents to is
x2 + y2 = a2 + b2
x2 - y2 = a2 - b2
x2 + y2 = a2 - b2
x2 - y2 = a2 + b2
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
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
Sum of the focal distance of an ellipse is equal to
2 b
2 a
2 ab
a + b
The eccentricity of the hyperbola x2 - 4y2 = 1 is
√5/2
√3/2
2/√5
2/√3
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
