Find the equation of the ellipse which crosses the point (-3,1) , and the multiply of the two distances between the point and the two focuses (foci) of the ellipse equals 6
For simplicity, let's assume the major axis lies along the x-axis, where the foci are at (-c,0) and (c,0), and .
If the product of the distances from the point (-3,1) to the foci is 6, then we may state:
Squaring gives:
Now solve this for .
Next, the equation of the ellipse may be written:
Since the ellipse passes through (-3,1), we may write:
where .
Using the value you found for , you may now solve for to find the equation of the ellipse.
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