The eccentricity of the conic 9 x2 - 16 y = 144 is
4/5
5/4
4/3
√7
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
The equation represents
an ellipse
a parabola
a hyperbola
a circle
The length of the latus rectum of the hyperbola is
2a2/b
2b2/a
b2/a
a2/b
Two diameters with slopes m1,m2 are conjugate if
m1m2 = -1
m1m2 = - b2/a2
m1m2 = a2/b2
m1m2 = b2/a2
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
The line y = 4x + c touches the hyperbola x2 - y2 = 1 iff
c = 0
c = ± √2
c = ± √15
c = ± √17
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
If e, e' are the eccentricities of hyperbolas and , then
e = e'
e = -e'
ee' = 1
1/e2 + 1/e'2 = 1
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
