Friday, January 13, 2017

College Algebra, Chapter 8, 8.2, Section 8.2, Problem 42

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=a2b2 and whose eccentricity is determined as e=ca. So, c=2 and if
ca=19, then

2a=19a=18

Thus,

c2=a2b2b2=a2c2b2=18222b2=320b=85

Therefore, the equation is
x2(85)2+y2(18)2=1 or x2320+y2324=1

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