The center of the ellipse $x^2+2y^2-4x+12y+14=0$ is

An ellipse,with foci at $(0, 2)$ and $(0, -2)$ and minor axis of length $4$,passes through which of the following points?

For real numbers $a, b$ $(a > b > 0)$,let $\text{Area} \{(x, y) : x^{2} + y^{2} \leq a^{2} \text{ and } \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} \geq 1\} = 30\pi$ and $\text{Area} \{(x, y) : x^{2} + y^{2} \geq b^{2} \text{ and } \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} \leq 1\} = 18\pi$. Then the value of $(a - b)^{2}$ is equal to

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

The minimum length of the intercept between the coordinate axes made by a tangent of the ellipse $\frac{x^2}{64}+\frac{y^2}{4}=1$ is

Find the equation for the ellipse that satisfies the given conditions: Length of minor axis $16$,foci $(0, \pm 6)$.