The eccentricity of the conic x2 - 2x - 4y2 = 0 is
1/4
3/2
√5/2
√5/4
For a hyperbola, the foci are at (±4, 0) and vertices at (±2, 0).Its equation is
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
√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 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
P is a point on the hyperbola , N is the foot of the⊥ from P on the transverse axis.The tangent to the hyperbola at P meets the transverse axis at T.If O is the centre of the hyperbola, then OT.ON is equal to
e2
a2
b2
b2/a2
If m is a variable , the locus of the point of intersection of the lines and is
a parabola
an ellipse
a hyperbola
a circle
If e, e' are the eccentricities of hyperbolas and , then
e = e'
e = -e'
ee' = 1
1/e2 + 1/e'2 = 1
The eccentricity of the conic 9x2 - 16y = 144 is
4/5
5/4
4/3
√7
