If the foci and vertices of an ellipse are $(\pm 1, 0)$ and $(\pm 2, 0)$ respectively,then the length of the minor axis of the ellipse is:

The foci of the ellipse $2x^2 + 3y^2 - 4x - 12y + 13 = 0$ are

For $\alpha$ belonging to an interval of length $\beta$,suppose $(\alpha, -\alpha)$ is an interior point of the ellipse $4x^2 + 5y^2 = 1$. Then,$(6\beta - 4)^{201} + 201 = $

The equation of the tangent to the curve $9x^{2} + 16y^{2} = 144$ which makes equal intercepts with the coordinate axes is:

For the ellipse $25x^2 + 9y^2 - 150x - 90y + 225 = 0$,the eccentricity $e$ is: (in $/5$)

If the line $y = 4x + c$ is a tangent to the ellipse $\frac{x^2}{8} + \frac{y^2}{4} = 1$,then $c = \dots$