Question 673090
what is the equation for this ellipse with a foci at (1,-4) and (-3,-4) and a length major axis at 12?
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Foci information show this is an ellipse with horizontal major axis.
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:
center: (-1,-4) (midpoint of x-coordinate and y-coordinate of foci)
given length of major axis=12=2a
a=6
a^2=36
c=2 (distance from center to foci on horizontal major axis)
c^2=4
c^2=a^2-b^2
b^2=a^2-c^2=36-4=32
Equation of given ellipse:
{{{(x+1)^2/36+(y+4)^2/32=1}}}