Question 1170524
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The standard form of the equation of an ellipse is<br>
{{{x^2/a^2-y^2/b^2 = 1}}}<br>
a is the length of the semi-major axis; b is the length of the semi-minor axis.<br>
a and b are related by<br>
{{{c^2 = a^2-b^2}}}<br>
where c is the distance from the center to each focus.<br>
The length of the major axis is the distance between the two extremes of the orbit.  In this problem, in units of millions of kilometers, the major axis is 420+580 = 1000.  So the semi-major axis a is 500.<br>
With the semi-major axis 500 and the minimum and maximum distances of the planet from the star being 420 and 580, the distance from the center to each focus is 80.<br>
So a=500 and c=80.<br>
(1) Use {{{c^2 = a^2-b^2}}} to determine b^2
(2) Write the equation using a^2 and b^2<br>