SOLUTION: Find the equation of the ellipse that the ends of the major axis at (-9,4) and (3,4) and passing through the point (-3,8).

Question 743730: Find the equation of the ellipse that the ends of the major axis at (-9,4) and (3,4) and passing through the point (-3,8).
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
You can get the and the center point from the major axis information. From -9 to +3 is , so . You can find from the two endpoints of the axis that the 'a' goes with the x, being horizontal major axis.

The center is on the line y=4 and is the midpoint of x at -9 and +3, so . Center is (-3,4).

Up to this, you have .
To finish, you want to use (-3,8) to find b.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the equation of the ellipse that the ends of the major axis at (-9,4) and (3,4) and passing through the point (-3,8).
***
This is an ellipse with horizontal major axis. (x-coordinates of major axis change but y-coordinates do not)
Its standard form of equation:, a>b, (h,k)=(x,y) coordinates of center.
For given ellipse:
x-coordinate of center=-3 (midpoint of -9 and 3)
y-coordnate of center=4
center: (-3,4)
length of horizontal major axis=12(-9 to 3)=2a
a=6
a^2=36
equation:
=0+16/b^2=1
b^2=16
b=4
Equation of given ellipse:

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