Equation of the ellipse with eccentricity $\frac{1}{2}$ and foci at $( \pm 1,\;0)$ is

Let $A,B$ and $C$ are three points on ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$where line joing $A \,\,\&\,\, C$ is parallel to the $x-$axis and $B$ is end point of minor axis whose ordinate is positive then maximum area of $\Delta ABC,$ is-

The foci of the ellipse $25{(x + 1)^2} + 9{(y + 2)^2} = 225$ are at

The equation of the ellipse whose foci are $( \pm 5,\;0)$ and one of its directrix is $5x = 36$, is

An ellipse has eccentricity $\frac{1}{2}$ and one focus at the point $P\left( {\frac{1}{2},\;1} \right)$. Its one directrix is the common tangent nearer to the point $P$, to the circle ${x^2} + {y^2} = 1$ and the hyperbola ${x^2} - {y^2} = 1$. The equation of the ellipse in the standard form, is

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse $\frac{x^{2}}{36}+\frac{y^2} {16}=1$