How many real tangents can be drawn to the ellipse $5x^2 + 9y^2 = 32$ from the point $(2,3)$
$2$
$1$
$0$
$3$
A focus of an ellipse is at the origin. The directrix is the line $x = 4$ and the eccentricity is $ \frac{1}{2}$ . Then the length of the semi-major axis is
If the area of the auxiliary circle of the ellipse $\frac{{{x^2}}}{{{a^2}}}\, + \,\frac{{{y^2}}}{{{b^2}}}\, = \,1(a\, > \,b)$ is twice the area of the ellipse, then the eccentricity of the ellipse is
Maximum length of chord of the ellipse $\frac{{{x^2}}}{8} + \frac{{{y^2}}}{4} = 1$, such that eccentric angles of its extremities differ by $\frac{\pi }{2}$ is
The equations of the directrices of the ellipse $16{x^2} + 25{y^2} = 400$ are
The eccentricity of the ellipse $25{x^2} + 16{y^2} = 100$, is