Suppose you would like to estimate the elliptical orbit of a certain object around the origin. observations are made of both an angle and a distance. you collect five observations as follows where the first value is degrees (counterclockwise from the positive x-axis) and the second is in millions of miles: (23◦ , ◦ , ◦ , ◦ , ◦ , 137) the equation of an ellipse in polar coordinates can be given by the following for some a and b where θ is the angle (counterclockwise from the positive x-axis) and r is distance from the origin: ar2 cos2 θ + br2 sin2 θ = 1 (a) find the least-squares best-fit ellipse. (b) use this to predict the distance of the object when θ = 225◦ . (c) what is the furthest that the object ever gets from the origin? hint: use sin2 θ + cos2 θ = 1