The ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ and the straight line $y = mx + c$ intersect in real points only if
${a^2}{m^2} < {c^2} - {b^2}$
${a^2}{m^2} > {c^2} - {b^2}$
${a^2}{m^2} \ge {c^2} - {b^2}$
$c \ge b$
If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is
An ellipse with its minor and major axis parallel to the coordinate axes passes through $(0,0),(1,0)$ and $(0,2)$. One of its foci lies on the $Y$-axis. The eccentricity of the ellipse is
Extremities of the latera recta of the ellipses $\frac{{{x^2}}}{{{a^2}}}\,\, + \,\,\frac{{{y^2}}}{{{b^2}}}\, = \,1\,$ $(a > b)$ having a given major axis $2a$ lies on
The angle between the pair of tangents drawn to the ellipse $3{x^2} + 2{y^2} = 5$ from the point $(1, 2)$, is
The length of the latus rectum of the ellipse $9{x^2} + 4{y^2} = 1$, is