The equation x = a cos θ, y = b sin θ, 0 ≤ θ < 2 π, a ≠ b, represent
an ellipse
a parabola
a circle
a hyperbola
Two diameters with slopes m1,m2 are conjugate if
m1m2 = -1
m1m2 = - b2/a2
m1m2 = a2/b2
m1m2 = 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
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 equation represents
The eccentricity of the conic 3x2 + 4y2 = 24 is
1/4
7/4
1/2
The equation of a directrix of the ellipse is
y = 25/3
x = 3
x = -3
x = 3/25
For the ellipse , the foci are
(± 1, 0)
(0, ± 1)
(± 1/√2, 0)
(± 1/2 , 0)
The sum of distance of any point on the ellipse 3x2 + 4y2 = 24 from its foci is.
8 √2
4 √2
16 √2
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
