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Write the equation of an ellipse with foci at (-6,-3) (0,-1) and a major axis of length 1.
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Let A be the point A = (-6,-3); let B be the point B = (0,-1).
The incremement of x-coordinate from A to B is 0-(-6) = 6 units.
The incremement of y-coordinate from A to B is -1-(-3) = 2 units.
The distance from A to B is = = ,
which is longer than 6 units.
Thus the distance between the given foci is greater than 6 units.
Then the major axis must be even LONGER than this value of 6 units.
But the problem says that the major axis is 1 unit.
This contradiction shows and proves that such ellipse does not exist.
Therefore, its equation can not be written.
