Question

Find the standard form or the equation of the ellipse with vertices (±7, 0) and eccentricity e=2/7

Answer 1

so
a=7
e = c/a = 2/7
solve for c

--> c/7 = 2/7
--> c = 2

now find b^2 where
b^2 +c^2 = a^2
b^2 + 4 = 49
b^2 = 45

ellipse equation:
\[\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\]