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 eccentricity of the hyperbola x2 - 4y2 = 1 is
√5/2
√3/2
2/√5
2/√3
For a hyperbola, the foci are at (±4, 0) and vertices at (±2, 0).Its equation is
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
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
Two diameters with slopes m1,m2 are conjugate if
m1m2 = -1
m1m2 = - b2/a2
m1m2 = a2/b2
m1m2 = b2/a2
The eccentricity of the conic 9x2 - 16y = 144 is
4/5
5/4
4/3
√7
The length of the latus rectum of the hyperbola is
2a2/b
2b2/a
b2/a
a2/b
The equation represents
an ellipse
a parabola
a hyperbola
a circle