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

The eccentricity of the curve represented by the equation ${x^2} + 2{y^2} - 2x + 3y + 2 = 0$ is

If the line $\frac{x}{a} + \frac{y}{b} = \sqrt{2}$ is tangent to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$,then its eccentric angle $\theta = ............^{\circ}$

The eccentricity of an ellipse having centre at the origin,axes along the coordinate axes and passing through the points $(4, -1)$ and $(-2, 2)$ is

The area of the greatest rectangle that can be inscribed in the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is

In an ellipse,the distance from one of the foci to its corresponding end of the major axis is $4-\sqrt{7}$ and the distance from the same focus to one end of the minor axis is $4$. Then the cosine of the angle subtended by the line segment joining its foci at one end of its minor axis is