Ellipse

The eccentricity of the ellipse whose major axis is three times the minor axis is:

The equation of the ellipse with focus at \((\pm 5,0)\) and $\(x=\frac{36}{5}\) as one directrix is

The condition for the line $l x+m y+n=0$ to be a normal to $\frac{x^2}{25}+\frac{y^2}{9}=1$ is

The area of the quadrilateral formed by the tangents at the end point of latusrectum to the ellipse $\frac{x^2}{9}+\frac{y^2}{5}=1$ is

The equation of the ellipse whose axes are parallel to the coordinate axes having its centre at the point $(2,-3)$ and focus at $(3,-3)$ and one vertex at $(4,-3)$ is

If the tangent to ellipse $x^2+2 y=1$ at point $P\left(\frac{1}{\sqrt{2}}, \frac{1}{2}\right)$ meets the auxiliary circle at the points $R$ and $Q$, then tangents to circle at $Q$ and $R$ intersect at

The radius of the circle passing through the foci of the ellipse $\frac{x^2}{4}+\frac{4 y^2}{7}=1$ and having its centre at $\left(\frac{1}{2}, 2\right)$ is

The eccentricity of the conic $x^2-4 x+4 y^2=12$ is

The locus of the extrimities of the latusrectum of the family of ellipses $b^2 x^2+y^2=a^2 b^2$ having a given major axis, is

If $P$ is a variable point on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, with $A A^{\prime}$ as major axis. Then, the maximum value of the area of the $\triangle A P A^{\prime}$ 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

The length of the axis of the conic $9 x^2+4 y^2-6 x+4 y+1=0$ are