# How do you write an equation of an ellipse in standard form given vertices (-5, 4) and (8, 4) and whose focus is (-4, 4)?

##### 1 Answer

#color(blue)((2x-3)^2/169+(y-4)^2/12=1)#

#### Explanation:

Given that the the coordinates of vertices of the ellipse are

The ordinates of vertices being same (4)the **axis of the ellipse is parallel to x-axis.**

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

#color(red)((x-1.5)^2/a^2+(y-4)^2/b^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-1.5)^2/6.5^2+(y-4)^2/12=1)#

#color(blue)(=>(2x-3)^2/169+(y-4)^2/12=1)#