Equations of ellipses Find an equation of the following ellipses, assuming the center is at the origin. Sketch a graph labeling the vertices and foci. Use a graphing utility to check your work.An ellipse with vertices (±5, 0), passing through the point (4, )

Solution 35EStep 1: Find an equation of the following ellipses, assuming the center is at the origin. Sketch a graph labeling the vertices and foci. Use a graphing utility to check your work.An ellipse with vertices , passing through the point Step 2:We know that the general formula for an ellipse with centre at the origin is The expression for vertices is .Thus from the question we have found the value of .Given the points .Thus we have and Therefore we can write the equation as The expression for foci is where Therefore Thus the focus is