The latus rectum of the ellipse 5x2 + 9y2 = 45 is
10/3
5/3
5√5/3
10√5/3
The sum of distance of any point on the ellipse 3x2 + 4y2 = 24 from its foci is.
8 √2
4 √2
16 √2
None of these
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
The distance of a focus of the ellipse 9x2 + 16y2 = 144 from an end of the minor axis is
3/2
3
4
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 equation of the ellipse with foci at (± 3, 0) and vertices at (± 5, 0) is
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
The locus of the point of intersection of perpendicular tangents to the ellipse is called
director circle
auxiliary circle
ellipse itself
similar ellipse
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 represents an ellipse iff
r > 2
r > 5
2 < r < 5
