The area of the region bounded by the curve $9x^2 + 4y^2 - 36 = 0$ is (in $\pi$)

The eccentricity of the ellipse $9x^2 + 5y^2 - 18x - 20y - 16 = 0$ is:

If $l$ and $b$ are respectively the length and breadth of the rectangle of greatest area that can be inscribed in the ellipse $x^2+4y^2=64$,then $(l, b) =$

If $A$ and $B$ are two fixed points and $P$ is a variable point such that $PA + PB = 4$,then the locus of $P$ is a/an

The equation of an ellipse in its standard form,given the distance between its foci is $2$ units and the length of its latus rectum is $\frac{15}{2}$ units,is

Let $P$ be a point on the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ and let the perpendicular drawn through $P$ to the major axis meet its auxiliary circle at $Q$. If the normals drawn at $P$ and $Q$ to the ellipse and the auxiliary circle respectively meet in $R$,then the equation of the locus of $R$ is