The line $x=m^2$ meets the ellipse $9x^2+y^2=9$ at real and distinct points if and only if

$A$ rectangle of maximum area is inscribed in an ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$. Then its dimensions are:

If $\alpha x+\beta y=109$ is the equation of the chord of the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$,whose midpoint is $\left(\frac{5}{2}, \frac{1}{2}\right)$,then $\alpha+\beta$ is equal to

The equation of the locus of a point $(2 \cos \theta-3, 3 \sin \theta-4)$ is

The sum of focal radii of the curve $9x^{2} + 25y^{2} = 225$ is

The normal at a point $P$ on the ellipse $x^2 + 4y^2 = 16$ meets the $x$-axis at $Q$. If $M$ is the midpoint of the line segment $PQ$,then the locus of $M$ intersects the latus rectum of the given ellipse at which points?