Question 689523
Write the standard equation for the ellipse with the given characteristics Foci: (5, 0), (-5, 0) Vertices: (9, 0), (-9, 0)
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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: (0,0)
a=9 (center to vertex on the major axis)
a^2=81
c=5 (center to foci on the major axis)
c^2=25
c^2=a^2-b^2
b^2=a^2-c^2=81-25=56
equation:
{{{x^2/81+y^2/56=1}}}