Question 740497
please help me find an equation for the ellipse that satisfies the given conditions.
Endpoints of minor axis (0, ±6), distance between foci 14
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Equation is that of an ellipse with horizontal major axis.
Its standard form: {{{(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)
b=6 (distance from center to end points of minor axis)
b^2=36
c=7 (distance from center to foci)
c^2=49
c^2=a^2-b^2
a^2=c^2+b^2=49+36=85
Equation of given ellipse:

 {{{x^2/85+y^2/36=1}}}