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
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
√5/2
√5/4
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
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
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 equation of the chord of the hyperbola x2 - y2 = 9 which is bisected at (5, -3) is
5x + 3y = 9
5x - 3y = 16
5x + 3y = 16
5x - 3y = 9
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
The length of the latus rectum of the hyperbola is
2a2/b
2b2/a
b2/a
a2/b
