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)?
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
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