Suppose you placed a grid on the plane of a comet's orbit, with the origin at the sun and the x-axis running through the longer axis of the orbit, as shown in the diagram. The table gives the approximate coordinates of the comet as it orbits the Sun. Both x and y are measured in astronomical units (AU).

a. Find an equation to fit these data.
b. Find the y-coordinate when the x-coordinate is 493.0 AU.
c. What is the greatest distance of the comet from the Sun?
d. What are the coordinates of the foci?

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Comet Sun x2. 2.9 62.6 244.5579.3 778.1 900.1 982.4 923.4 663.0 450.0 141.6 y 5.5 16.3 31.5 54.6 62.051.636.1 10.9-31.5-59.262.844.5