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 locus of mid-points of the line segments joining $\left(-3,-5\right)$and the points on the ellipse $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$is :

Paragraph: Consider the following for the next two (02) items that follow: $\mathrm{P}(x, y)$ is any point on the ellipse $x^2+4 y^2=1$. Let $E, F$ be the foci of the ellipse. Question: What is $P E+P F$ equal to?

The length of latus rectum of the ellipse $4 x^2+9 y^2=36$ is

The position of the point $(1,2)$ relative to the ellipse $2 \mathrm{x}^2+7 \mathrm{y}^2=20$ is

What is the sum of the focal distances of a point of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ ?

What is the eccentricity of the conic $4 x^2+9 y^2=144$ ?

The sum of the focal distances of a point on the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ is :

Let $P$ be any point on the ellipse $7x^{2}+16y^{2}=112,S$ be a focus, $L$ be the correspondingdirectrix and $PM$ be the perpendicular distance from $P$ to directrix $L$. Then $\frac{SP}{PM}=$

The equation of an ellipse in its standard form, given the distance between its foci is 2 units and the length of its latusrectum is $\frac{15}{2}$ units, is

The lengths of the sides of the rectangle of greatest area that can be inscribed in the ellipse \(x^2+4 y^2=64\) are