SOLUTION: Endpoints of major axis at (−4, 2) and (12, 2); endpoints of the minor axis at (4, 4) and (4, 0) . finding the general form

Question 1165933: Endpoints of major axis at (−4, 2) and (12, 2); endpoints of the minor axis at (4, 4) and (4, 0) . finding the general form
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Don't use special characters in your posts. Fortunately, it is obvious from the rest of the given information that the first endpoint of the major axis is (-4,2).

This is an ellipse with horizontal major axis; the general form is

(h,k) is the center; a is the semi-major axis; b is the semi-minor axis.

The length of the major axis is 16 (from (-4,2) to (12,2)), so the semi-major axis is 8.

The length of the minor axis is 4 (from (4,4) to (4,0)), so the semi-minor axis is 2.

To find the center (h,k), you can use the midpoint of either the major or minor axis; those midpoints are (4,2).

Note you can also find the center by noting that the major axis is on the line y=2 and the minor axis is on the line x=4 -- making the intersection of the axes at (4,2).

So we have (h,k) = (4,2); a=8; b=2.

So the equation is

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