Ellipse

The sum of distances of any point on the ellipse $\frac{x^2}{4}+\frac{y^2}{3}=1$ from its two directrix is

Let $P$ be a variable point on the ellipse $\frac{x^2}{5+2\sqrt{3}}+\frac{y^2}{15}=1$ with foci $F_1$ & $F_2$. If the maximum area of the triangle $P{F}_1{F}_2$ is equal to one third the area of the ellipse. The eccentricity of the ellipse is

Find the equation of ellipse with centre at origin, major axis on the $x$-axis and satisfying 
Length of major axis $=8$ and eccentricity$=\frac{1}{2}$

Find the equation of ellipse having foci at $(\pm 3,0),$ passing through$(4,1)$.

Find the equation of ellipse having foci at $(0,\pm 4), e=\frac{4}{5}$.

Find the equation of ellipse satisfying that the vertices at $(0,\pm 10),e=\frac{4}{5}$

Find the co-ordinates of the foci of the ellipse $\frac{x^2}{36}+\frac{y^2}{49}=1$

Find the co-ordinates of the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{4}=1$

The sum of lengths of major axis and minor axis of an ellipse  $4x^2+y^2=100$ is 

The sum of lengths of major axis and minor axis of the ellipse  $4x^2+9y^2=36$ is

Find the equation of the ellipse whose major axis coincides with $x=1$, centre is $\left(1,5\right)$, one focus is $\left(1,8\right)$ and the sum of focal distances of a point on the ellipse is $12$?

Find the equation of the ellipse having its centre at $\left(2,-3\right)$, one focus at point $\left(3,-3\right)$ and vertex at $\left(4,-3\right)$.

Find the eccentricity of the ellipse whose foci are $\left(-2,4\right)$ and $\left(4,4\right)$ and whose major axis is $10$.

Find the equation of the ellipse whose foci are $\left(-1,5\right)$ and $\left(5,5\right)$ and whose major axis is $10$.

Find the equation of the ellipse whose vertices are $\left(-1,2\right)$ and $\left(9,2\right)$ and whose eccentricity is $\frac{4}{5}$.

Find the equation of the ellipse whose centre is at $\left(-2,3\right)$ and whose lengths of the semi-axes are $3$ and $2$ when major axis is parallel to $y-$axis.

The eccentricity of the ellipse $\frac{{\left(x - 1\right)}^2}{2}+{\left(y+\frac{3}{4}\right)}^2=\frac{1}{16}$ is

The coordinates of points $A$ and $B$ shown on a ellipse, whose equation is given by $4x^2+9y^2=36,$ are :-

Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(b<a),$ be an ellipse with major axis $AB$ and minor axis $CD.$ Let $F_1$ and $F_2$ be its two foci, with $A,F_1, F_2, B$ in that order on the segment $AB.$ Suppose $\angle F_{1}CB=90°.$ The eccentricity of the ellipse is

Find the equation of the ellipse whose center is at the origin, foci are at $\left(2,0\right)$, and $\left(-2,0\right)$ respectively and eccentricity is $\frac{1}{\sqrt{2}}$.