The eccentricity of the ellipse $4x^2 + 9y^2 + 8x + 36y + 4 = 0$ is

If the distance between the foci of an ellipse is $6$ and the length of the minor axis is $8$,then the eccentricity is

If tangents are drawn to the ellipse $x^2+2y^2=2$,then the locus of the midpoints of the intercepts made by the tangents between the coordinate axes is

Let a line $L$ pass through the point of intersection of the lines $bx + 10y - 8 = 0$ and $2x - 3y = 0$,where $b \in R - \{\frac{4}{3}\}$. If the line $L$ also passes through the point $(1, 1)$ and touches the circle $17(x^2 + y^2) = 16$,then the eccentricity of the ellipse $\frac{x^2}{5} + \frac{y^2}{b^2} = 1$ is:

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:

If $OB$ is the semi-minor axis of an ellipse,$F_1$ and $F_2$ are its foci and the angle between $F_1B$ and $F_2B$ is a right angle,then the square of the eccentricity of the ellipse is