Determine the equation for the ellipse with eccentricity 19 and foci (0,±2)
The equation x2b2+y2a2=1 is an ellipse with vertices major axis with foci (0,±c)
where c2=a2−b2 and whose eccentricity is determined as e=ca. So, c=2 and if
ca=19, then
2a=19a=18
Thus,
c2=a2−b2b2=a2−c2b2=182−22b2=320b=8√5
Therefore, the equation is
x2(8√5)2+y2(18)2=1 or x2320+y2324=1
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