The equations represent
a circle
an ellipse
a parabola
a hyperbola
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
None of these
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 latus rectum of the ellipse 5x2 + 9y2 = 45 is
10/3
5/3
5√5/3
10√5/3
Sum of the focal distance of an ellipse is equal to
2 b
2 a
2 ab
a + b
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 eccentricity of an ellipse whose latus rectum is half of its major axis is
1/√2
√3/2
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
