Question

find the standard form of the equation of an ellipse that has a major axis of length 6 and fox at (-2,0) and (2,0)

Answer 1

let the equation be $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
because the length of major axis is 6, 2a=6. then a=3, a²=9.
c=2, $a^2-b^2=c^2$, so $b^2=5$
therefore, the equation is $\frac{x^2}9+\frac{y^2}5=1$

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