The orbit of a planet around the sun is not circular; it is an ellipse with the Sun at one focus. The aphelion of a planet is the greatest distance from the sun and the perihelion is its shortest distance. The mean distance of a planet from the sun is the length of the semimajor axis of the elliptical orbit. The perihelion of Pluto is 4551 million miles, and the distance from the center of its elliptical orbit to the sun is 897.5 million miles. Find the aphelion of Pluto. What is the mean distance of Pluto from the Sun? Write an equation to represent the orbit of Pluto around the Sun.

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.