document.write( "Question 1167713: 1. Kepler observed that Pluto orbits the sun in an elliptic motion. With the
\n" ); document.write( "sun at one focus, nearest that Pluto gets to the Sun is 4,400,000,000 km, and the farthest that it goes to the Sun is 7,400,000,000 km. \r
\n" ); document.write( "\n" ); document.write( "a) Assuming that the center of Pluto’s orbit is at (0, 0), find the equation
\n" ); document.write( "that models Pluto’s orbit.
\n" ); document.write( "b) If an unidentified planet is located in the other focus, how far is this
\n" ); document.write( "planet from the Sun? \n" ); document.write( "
Algebra.Com's Answer #851757 by htmentor(1343)\"\" \"About 
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The equation for an ellipse centered at the origin is x^2/a^2 + y^2/b^2 = 1, where a, b are the semi-major and semi-minor axes, respectively.
\n" ); document.write( "The sun is located at one focus with coordinates (-c,0), with c^2 = a^2 - b^2.
\n" ); document.write( "For simplicity, we will express the distances in billions of miles.
\n" ); document.write( "The distance of the furthest approach is 7.4 = c + a, and the closest
\n" ); document.write( "approach is 4.4 = a - c. Solving for a gives 2a = 11.8 -> a = 5.9.
\n" ); document.write( "Solving for c gives 2c = 3 -> c = 1.5.
\n" ); document.write( "b^2 = a^2 - c^2 -> b^2 = 5.9^2 - 1.5^2 = 32.56.
\n" ); document.write( "Thus, the equation is x^2/34.81 + y^2/32.56 = 1.
\n" ); document.write( "If another planet is placed at the other focus, the distance between them
\n" ); document.write( "will be 2c = 3.
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