The equation of tangent and normal at point $(3, -2)$ of ellipse $4{x^2} + 9{y^2} = 36$ are
$\frac{x}{3} - \frac{y}{2} = 1,\;\frac{x}{2} + \frac{y}{3} = \frac{5}{6}$
$\frac{x}{3} + \frac{y}{2} = 1,\;\frac{x}{2} - \frac{y}{3} = \frac{5}{6}$
$\frac{x}{2} + \frac{y}{3} = 1,\;\frac{x}{3} - \frac{y}{2} = \frac{5}{6}$
None of these
In an ellipse the distance between its foci is $6$ and its minor axis is $8$. Then its eccentricity is
The length of the axes of the conic $9{x^2} + 4{y^2} - 6x + 4y + 1 = 0$, are
An ellipse has $OB$ as semi minor axis, $F$ and $F'$ its foci and the angle $FBF'$ is a right angle. Then the eccentricity of the ellipse is
The smallest possible positive slope of a line whose $y$-intercept is $5$ and which has a common point with the ellipse $9 x^2+16 y^2=144$ is
Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse $9 x^{2}+4 y^{2}=36$.