Question 1136776
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Since you asked for help, that's exactly what I will do -- show you what you need to do to find the equation.  Then, doing the work yourself, you will learn something from it.<br>
The standard form of the equation of an ellipse with horizontal major axis centered at (h,k) is<br>
{{{(x-h)^2/a^2+(y-k)^2/b^2 = 1}}}<br>
In that formula, a is the semi-major axis (from the center of the ellipse to each end of the major axis) and b is the semi-minor axis (from the center to each end of the minor axis).<br>
The two given vertices are the ends of the major axis; from that information you can determine the center of the ellipse (halfway between the two vertices) and the value of a (distance from the center to each vertex).<br>
The only thing left you need to write the equation is the value of b.<br>
The distance from the center of the ellipse to each focus is c, where a, b, and c are related by<br>
{{{c^2 = a^2-b^2}}}<br>
Since you now know the center of the ellipse, the given coordinates of a focus allow you to determine the value of c; and from that you can determine the value of b.<br>
Then you will have all you need to write the equation.<br>
Good luck finishing.<br>
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