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).
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This is an ellipse with horizontal major axis. (x-coordinates of major axis change but y-coordinates do not)
Its standard form of equation:{{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}, 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:{{{(-3-(-3))^2/36+(8-4)^2/b^2=1}}}
=0+16/b^2=1
b^2=16
b=4
Equation of given ellipse:
{{{(x+3)^2/36+(y-4)^2/16=1}}}