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

The eccentricity of an ellipse centered at the origin is $1/2$. If one of its directrices is $x = 4$,then the equation of the ellipse is:

An arch is in the form of a semi-ellipse. It is $8 \, m$ wide and $2 \, m$ high at the centre. Find the height of the arch at a point $1.5 \, m$ from one end. (in $, m$)

If $\alpha$ and $\beta$ are the eccentric angles of the endpoints of a focal chord of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,then $\tan \frac{\alpha}{2} \tan \frac{\beta}{2} = ....$

If the eccentricities of the two ellipses $\frac{x^2}{169} + \frac{y^2}{25} = 1$ and $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ are equal,then the value of $a/b$ is

The coordinates of the foci of the ellipse $16x^{2} + 9y^{2} = 144$ are