If e and e1 are the eccentricities of the hyperbolas xy = c2 and x2 - y2 = c2 , then e2 + e21 is equal to
1
4
6
8
The diameter of 16 x2 - 9 y2 = 144 which is conjugate to x = 2 y is
y = 16/9 x
y = 32/9 x
x = 16/9 y
x = 32/9 y
For a hyperbola, the foci are at (±4, 0) and vertices at (±2, 0).Its equation is
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
If the chords of contact of tangents from two points (x1,y1) and (x2,y2) to the hyperbola are at right angles, then is equal to
-a2/b2
-b2/a2
-b4/a4
-a4/b4
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 eccentricity of the conic 9 x2 - 16 y = 144 is
4/5
5/4
4/3
√7
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
The equation represents
an ellipse
a parabola
a hyperbola
a circle