The number of values of $c$ such that line $y = cx + c$, $c \in R$ touches the curve $\frac{{{x^2}}}{4} + \frac{{{y^2}}}{1} = 1$ is
$0$
$1$
$2$
more than $2$
If tangents are drawn to the ellipse $x^2 + 2y^2 = 2$ at all points on the ellipse other than its four vertices than the mid points of the tangents intercepted between the coordinate axes lie on the curve
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
On the ellipse $\frac{{{x^2}}}{{18}} + \frac{{{y^2}}}{8} = 1$ the point $M$ nearest to the line $2x - 3y + 25 = 0$ is
The length of the latus rectum of the ellipse $\frac{{{x^2}}}{{36}} + \frac{{{y^2}}}{{49}} = 1$
The eccentricity of the ellipse $\frac{{{{(x - 1)}^2}}}{9} + \frac{{{{(y + 1)}^2}}}{{25}} = 1$ is