The locus of the centre of the circle x2 + y2 + 4x cos θ - 2y sin θ - 10 = 0 is
an ellipse
a circle
a hyperbola
a parabola
The distance of a focus of the ellipse 9x2 + 16y2 = 144 from an end of the minor axis is
3/2
3
4
None of these
The eccentricity of the conic 3x2 + 4y2 = 24 is
1/4
7/4
1/2
The equation of the ellipse whose focus is (1, -1),directrix x - y - 3 = 0 and eccentricity 1/2 is
7x2 + 2xy + 7y2 - 10x + 10y + 7 = 0
7x2 + 2xy + 7y2 + 7 = 0
7x2 + 2xy + 7y2 + 10x - 10y - 7 = 0
The equations represent
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
The equation of the ellipse with foci at (± 3, 0) and vertices at (± 5, 0) is
The latus rectum of the ellipse 5x2 + 9y2 = 45 is
10/3
5/3
5√5/3
10√5/3
The equation of a directrix of the ellipse is
y = 25/3
x = 3
x = -3
x = 3/25
The equation x = a cos θ, y = b sin θ, 0 ≤ θ < 2 π, a ≠ b, represent
