Ellipse

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

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

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

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 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 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

Tangent to the ellipse $\frac{x^2}{32}+\frac{y^2}{18}=1$ having slope $\frac{-3}{4}$ meet the coordinate axis at $A$ and $B$. Then, the area of $\triangle A O B$, where $O$ is the origin, is

The minimum radius vector of the curve $\frac{a^2}{x^2}+\frac{b^2}{y^2}=1$ is of length

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

The number of real tangents that can be drawn to the ellipse $3 x^2+5 y^2=32$ passing through $(3,5)$ is

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