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 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 equation represents an ellipse iff
r > 2
r > 5
2 < r < 5
None of these
The equation of the ellipse with foci at (± 3, 0) and vertices at (± 5, 0) is
The eccentricity of the conic 3x2 + 4y2 = 24 is
1/4
7/4
1/2
The line y = 2x + c touches the ellipse if c is equal to
0
± 2 √17
c = ± √15
c = ± √17
The locus of the point of intersection of perpendicular tangents to the ellipse is called
director circle
auxiliary circle
ellipse itself
similar ellipse
Sum of the focal distance of an ellipse is equal to
2 b
2 a
2 ab
a + b
The equation of a directrix of the ellipse is
y = 25/3
x = 3
x = -3
x = 3/25
The line x cos α + y sin α = P is tangent to the ellipse if
a2 cos2 α - b2 sin2 α = P2
a2 sin2 α + b2 cos2 α = P2
a2cos2 α + b2 sin2 α = P2
a2cos2 α + b2 sin2 α = P
