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 length of the latus rectum of the hyperbola is
2a2/b
2b2/a
b2/a
a2/b
The equations of the transverse and conjugate axes of a hyperbola respectively are x + 2 y - 3 = 0, 2 x - y + 4 = 0 and their respective length are √2 and 2/√3. The equation of the hyperbola is.
2/5 ( x + 2 y - 3)2 - 3/5 (2 x - y + 4)2 = 1
2/5 (2 x - y + 4)2 - 3/5 (x + 2 y - 3)2 = 1
2 (2 x - y + 4 )2 - 3 (x + 2 y - 3)2 = 1
2 (x + 2 y - 3)2 - 3 (2 x - y + 4)2 = 1
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
The equation represents
an ellipse
a parabola
a hyperbola
a circle
The equation of the chord of the hyperbola x2 - y2 = 9 which is bisected at (5, -3) is
5 x + 3 y = 9
5 x - 3 y = 16
5 x + 3 y = 16
5 x - 3 y = 9
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
The eccentricity of the hyperbola x2 - 4y2 = 1 is
√5/2
√3/2
2/√5
2/√3
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
