?Find an equation of the ellipse. Then find its foci

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 \(\dfrac{{{x}^{2}}}{4}+\dfrac{{{y}^{2}}}{9}=1\).