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 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 9 x2 - 16 y = 144 is
4/5
5/4
4/3
√7
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 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 conic x2 - 2 x - 4 y2 = 0 is
1/4
3/2
√5/2
√5/4
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
If the normal at (ct, c/t) on the curve xy = c2 meets the curve again in t' , then
t' = -1/t3
t' = -1/t
t' = 1/t2
t'2 = -1/t2
