The line $lx + my + n = 0$is a normal to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, if
$\frac{{{a^2}}}{{{m^2}}} + \frac{{{b^2}}}{{{l^2}}} = \frac{{({a^2} - {b^2})}}{{{n^2}}}$
$\frac{{{a^2}}}{{{l^2}}} + \frac{{{b^2}}}{{{m^2}}} = \frac{{{{({a^2} - {b^2})}^2}}}{{{n^2}}}$
$\frac{{{a^2}}}{{{l^2}}} - \frac{{{b^2}}}{{{m^2}}} = \frac{{{{({a^2} - {b^2})}^2}}}{{{n^2}}}$
None of these
The length of the latus rectum of the ellipse $5{x^2} + 9{y^2} = 45$ is
Let the maximum area of the triangle that can be inscribed in the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{4}=1$, a $>2$, having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the $y$-axis, be $6 \sqrt{3}$. Then the eccentricity of the ellispe is
Let $P(2,2)$ be a point on an ellipse whose foci are $(5,2)$ and $(2,6)$, then eccentricity of ellipse is
If the tangent at a point on the ellipse $\frac{{{x^2}}}{{27}} + \frac{{{y^2}}}{3} = 1$ meets the coordinate axes at $A$ and $B,$ and $O$ is the origin, then the minimum area (in sq. units) of the triangle $OAB$ is
If the length of the latus rectum of the ellipse $x^{2}+$ $4 y^{2}+2 x+8 y-\lambda=0$ is $4$ , and $l$ is the length of its major axis, then $\lambda+l$ is equal to$......$