The eccentricity of the conic 9x2 - 16y = 144 is
4/5
5/4
4/3
√7
The equations of the transverse and conjugate axes of a hyperbola respectively are x + 2y - 3 = 0, 2x - y + 4 = 0 and their respective length are √2 and 2/√3. The equation of the hyperbola is.
2/5 ( x + 2y - 3)2 - 3/5 (2x - y + 4)2 = 1
2/5 (2x - y + 4)2 - 3/5 (x + 2y - 3)2 = 1
2 (2x - y + 4 )2 - 3 (x + 2y - 3)2 = 1
2 (x + 2y - 3)2 - 3 (2x - y + 4)2 = 1
The eccentricity of the hyperbola x2 - 4y2 = 1 is
√5/2
√3/2
2/√5
2/√3
The equation represents
an ellipse
a parabola
a hyperbola
a circle
A point moves in a plane so that its distances PA and PB from two fixed points A and B in the plane satisfy the relation PA - PB = K (K ≠ 0), then the locus of P is.
a branch of a hyperbola
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
If e, e' are the eccentricities of hyperbolas and , then
e = e'
e = -e'
ee' = 1
1/e2 + 1/e'2 = 1
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 eccentricity of the conic x2 - 2x - 4y2 = 0 is
1/4
3/2
√5/4