In this problem, you will use Newton’s method to estimate the locations of the points of intersection of the ellipses having equations 3x2 + y2 = 7 and x2 + 4y2 = 8.
(a) Graph the ellipses and use your graph to give a very rough estimate (x0, y0) of the point of intersection that lies in the first quadrant.
(b) Denote the exact point of intersection in the first quadrant by (X, Y). Without solving, argue that the other points of intersection must be (−X, Y), (X, −Y), and (−X, −Y).
(c) Now use Newton’s method with your estimate (x0, y0) in part (a) to approximate the first quadrant intersection point (X, Y ).
(d) Solve for the intersection points exactly, and compare your answer with your approximations.
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