The length of the latus rectum of the hyperbola is
2a2/b
2b2/a
b2/a
a2/b
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
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
The latus rectum of the ellipse 5x2 + 9y2 = 45 is
10/3
5/3
5√5/3
10√5/3
The equation ax2 + 2 hxy + by2 + 2 gx + 2 fy + c = 0 represents an ellipse if
Δ =0, h2 < ab
Δ ≠ 0, h2 < ab
Δ ≠ 0, h2 > ab
Δ ≠ 0, h2 = ab
Two diameters with slopes m1,m2 are conjugate if
m1m2 = -1
m1m2 = - b2/a2
m1m2 = a2/b2
m1m2 = b2/a2
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 eccentricity of the hyperbola x2 - 4y2 = 1 is
√5/2
√3/2
2/√5
2/√3
The line y = 2x + c touches the ellipse if c is equal to
0
± 2 √17
c = ± √15
c = ± √17
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