Question

Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); y-intercepts: -5 and 5

Answer 1

Using your standard equation of an ellipse for b>a:
\[\large \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]
Where:
"a" is the minor axis
"b" is the major axis
In your question, you're given the coordinates of the foci, S, and y-intercepts i.e the value of "b".
\[\large S(0, \pm be)\]
where:
"e" is the eccentricity
\[\large y=\pm 5\]
By connecting the-coordinates of the foci and the y-intercepts, you can find the value of "e".
Let's take the positive case for both the foci and y-intercepts.
Therefore:
\[be=2\]
\[b=5\]
\[5e=2\]
\[e=\frac{2}{5}\]

Answer 2

By connecting the y-coordinates*

Answer 3

By using this equation:
\[a^2=b^2(1-e^2)
You can find the value of "a" and thus form your standard equation of the ellipse.

Answer 4

\[a^2=b^2(1-e^2)\]

Answer 5

Thanks