The line $12 x \cos \theta + 5 y \sin \theta = 60$ is tangent to which of the following curves?

In an ellipse,the distance between its foci is $6$ and the minor axis is $8$. Then its eccentricity is:

If the chord through the points whose eccentric angles are $\theta$ and $\phi$ on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ passes through the focus,then the value of $(1 + e) \tan(\frac{\theta}{2}) \tan(\frac{\phi}{2})$ is

If $m$ is the length of the latus rectum and $n$ is the length of the major axis of the ellipse $25x^2+16y^2-150x-64y-111=0$,then the ordered pair $(m, n) =$

Chords of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ are drawn through the positive end of the minor axis $(0, b)$. The locus of their midpoints lies on:

$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ $(b > a)$ is an ellipse with eccentricity $e = \frac{1}{\sqrt{2}}$. If the angle of intersection between the ellipse and the parabola $y^2 = 4ax$ is $\theta$,then the coordinates of the point corresponding to $\theta$ on the ellipse are: