$\"\"$ \ \

\

Foci : $\"\"$ .

\

Passing through the point $\"\"$ .

\

Since the $\"\"$ -coordinates of the foci are same, the ellipse is horizontal.

\

The standard form of horizontal ellipse is $\"\"$ , \ \

\

where $\"\"$ , $\"\"$ ,

\

$\"\"$ : length of semi major axis, $\"\"$ : length of semi minor axis, \ \

\

Center : $\"\"$ , Foci : $\"\"$ , \ \

\

Vertices : $\"\"$ , co-vertices : $\"\"$ , \ \

\

Major axis : $\"\"$ , Minor axis : $\"\"$ .

\

$\"\"$

\

The center of the ellipse is the mid point of the foci.

\

So, $\"\"$ . \ \

\

The distance between the foci is equals to $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

Find the values of $\"\"$ and $\"\"$ .

\

Consider $\"\"$ .

\

$\"\"$ \ \

\

$\"\"$ \ \

\

$\"\"$ .

\

The ellipse equation is passing through the point $\"\"$ .

\

Substitute $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The solutions of equation is $\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ and $\"\"$

\

$\"\"$ and $\"\"$

\

$\"\"$ and $\"\"$ .

\

$\"\"$ is does not a valid solution.

\

Therefore, $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Substitute the values $\"\"$ , $\"\"$ and $\"\"$ in standard form of horizontal ellipse.

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

The ellipse equation is $\"\"$ . \ \