# How do you write an equation of an ellipse in standard form given foci are (-2,1) and (-2,5) and vertices are (-2,-1) and (-2,7)?

##### 1 Answer

#color(blue)((x+2)^2/12+(y-3)^2/16=1)#

#### Explanation:

Given that the the coordinates of vertices of the ellipse are

The abscissas of vertices being same (-2)the **axis of the ellipse is parallel to y-axis.So the major axis is parallel to y-axis**

*If a and b are halves of the major axis and minor axis respectively then the standard equation of ellipse may be written as*

#color(red)((x+2)^2/b^2+(y-3)^2/a^2=1)..... (1)#

Now we are to findout a and b.

Again it is also given the coordinate of

Now **a** is the distance between center and vertex.

Now if **e** represnts eccentricity of the ellipse then

Now the distance between center and focus is **ae**

Now inserting the value of a and b in equation (1) we get the equation of ellipse as

#color(blue)((x+2)^2/12+(y-3)^2/16=1)#