A satellite in a 100-mile-high circular orbit around the Earth has a velocity of approximately 17,500 miles per hour. When this velocity is multiplied by √2, the satellite has the minimum velocity necessary to escape Earth’s gravitational pull and follow a parabolic path with the center if Earth as the focus. Assume that the radius of the Earth is 4000 miles.  1) Find the escape velocity of the weather satellite.  2) Find the standard equation of the parabolic path of the weather satelli

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A: To show that the equation represents a sphere, and find its center and radius: 2x2+2y2+2z2=8x-24z+1

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A: The solution is below.

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