Question

Find the equation for the ellipse that satisfies the given conditions:
Vertices $(\pm 5,0)$, foci $(\pm 4,0)$

• A. $\frac{x^2}{25}+\frac{y^2}{9}=1$
• B. $\frac{x^2}{9}+\frac{y^2}{25}=1$
• C. $\frac{x^2}{25}-\frac{y^2}{9}=1$
• D. $\frac{x^2}{2}+\frac{y^2}{9}=1$

Answer 1

Answer: (A)

$\frac{x^2}{25}+\frac{y^2}{9}=1$

$a=5andae=4\therefore e=\left(\frac{4}{a}\right)=\left(\frac{4}{5}\right)as{e}^2{a}^2=a^2-b^2\therefore b^2=a^2(1-e^2)b^2=25(1-(\frac{16}{25}\left)\right)b^2=25\times \left(\frac{9}{25}\right)\therefore b=3\therefore equationofellipseis\left(\frac{x^2}{25}\right)+\left(\frac{y^2}{9}\right)=1$