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?Find an equation of the ellipse. Then find its foci
Chapter 9, Problem 17(choose chapter or problem)
Find an equation of the ellipse. Then find its foci.
Questions & Answers
QUESTION:
Find an equation of the ellipse. Then find its foci.
ANSWER:
Step 1 of 2
Consider the equation of the ellipse as follows.
\(\dfrac{{{x}^{2}}}{{{a}^{2}}}+\dfrac{{{y}^{2}}}{{{b}^{2}}}=1\) ………..(1)
Where y intercepts are \pm a, and x intercepts are \(\pm\) b.
From figure we see that y intercepts are \pm 3 and x intercepts are \(\pm\) 2.
Substitute the above values into the equation of the ellipse as follows.
(1) \(\dfrac{{{x}^{2}}}{{{\left( \pm 2 \right)}^{2}}}+\dfrac{{{y}^{2}}}{{{\left( \pm 3 \right)}^{2}}}=1\)
(2) \( \dfrac{{{x}^{2}}}{4}+\dfrac{{{y}^{2}}}{9} =1\)
Hence, the equation of the ellipse is \(\dfrac{{{x}^{2}}}{4}+\dfrac{{{y}^{2}}}{9}=1\).