Question

An ellipse has vertex (0, 4), co-vertex (3, 0) and is centered at the origin. What is the equation for the ellipse?

Answer 1

Answer:

Step-by-step explanation:

Notice: The first vertex (0, 4) is further from the origin than is the second vertex (3, 0), in the y-direction and the x-direction, respectively.

The standard equation of an ellipse with center at the origin is

 x²         y²

------ + ------ = 1  

 a²       b²

and a represents the greater distance from the origin to one covertex or the other.  In this case we let a = 4 and b = 2. Then we have:

y²      x²

---- + ------ = 1     which is the equation of this ellipse in final

4²      3²                                    finished form.