Write the equation of the ellipse centered at the origin with a vertex at (5,0) and a co-vertex at (0,4).

Answer 1

The equation of an ellipse is (x-h)²/a² + (x-k)²/b² = 1 . The point (h,k) is the center of the ellipse. In this case (h,k) = (0,0) because the ellipse is centered at the origin.

The value 'a' can be either the distance from the center to the vertex or from the center to the co-vertex. It depends on which one is displaced in the x-direction because 'a' is in the denominator of the x term. In that case 'a' is 5 because the vertex is displaced horizontally by 5 from the center. Under that same logic b is 4 because the co-vertex is displaced vertically from center by a distance of 4.

Sub all the values in and you will have your equation.