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)?
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
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