Length of common chord of the ellipse ${\frac{{\left( {x - 2} \right)}}{9}^2} + {\frac{{\left( {y + 2} \right)}}{4}^2} = 1$ and the circle ${x^2} + {y^2} - 4x + 2y + 4 = 0$
$0$
$\frac{1}{{\sqrt 2 }}$
$1$
${\kern 1pt} \sqrt 2 $
If distance between the directrices be thrice the distance between the foci, then eccentricity of ellipse is
If the distance between the foci of an ellipse be equal to its minor axis, then its eccentricity is
The line, $ lx + my + n = 0$ will cut the ellipse $\frac{{{x^2}}}{{{a^2}}}$ $+$ $\frac{{{y^2}}}{{{b^2}}}$ $= 1 $ in points whose eccentric angles differ by $\pi /2$ if :
The eccentricity of an ellipse is $2/3$, latus rectum is $5$ and centre is $(0, 0)$. The equation of the ellipse is
The equation of normal at the point $(0, 3)$ of the ellipse $9{x^2} + 5{y^2} = 45$ is