Find the equation of the ellipse whose major axis is $8$ and eccentricity is $1/2$ $(a > b)$.

The locus of a point such that the sum of its distances from the points $(0, 2)$ and $(0, -2)$ is $6$ is:

An angle of intersection of the curves,$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ and $x^{2}+y^{2}=ab$,where $a > b$,is :

The equation of an ellipse whose focus is $(-1, 1)$,whose directrix is $x - y + 3 = 0$,and whose eccentricity is $e = \frac{1}{2}$,is given by

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

Let $P$ be an arbitrary point on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ where $a > b > 0$. Suppose $F_1$ and $F_2$ are the foci of the ellipse. The locus of the centroid of the $\triangle P F_1 F_2$ as $P$ moves on the ellipse is