to divide quarter of an ellipse into two equal halves

Question

I wanted to divide the quarter of an ellipse into two equal halves. In what angle should I divide it so that both the arcs formed are equal in length. Finally I wanted to find the midpoint of the arc of a quarter of ellipse. Any hint will be a privilege. Thanks in advance, Regards

Answer 1

Take one point on ellipse as (rcos $\alpha$ ,rsin $\alpha$ ).Find area using integration.using proper limits of both parts and equate it.You will get one triangular region and one region you have to solve using definite interation with proper limits for each part.Is that enough or do you need more hint?