Question

Equation of the ellipse $e=\frac{4}{5}$ is:

• A. $9x^2+25y^2=225$
• B. $25x^2+9y^2=225$
• C. $\frac{x^2}{36}+\frac{y^2}{100}=1$
• D. $\frac{x^2}{100}+\frac{y^2}{36}=1$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $9x^2+25y^2=225$
B $\frac{x^2}{36}+\frac{y^2}{100}=1$
C $25x^2+9y^2=225$
D $\frac{x^2}{100}+\frac{y^2}{36}=1$

verify eccentricity
A) $e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{9}{25}}=\frac{4}{5}$
B) $e=\sqrt{1-\frac{a^2}{b^2}}=\sqrt{1-\frac{9}{25}}=\frac{4}{5}$
C) $e=\sqrt{1-\frac{a^2}{b^2}}=\sqrt{1-\frac{36}{100}}=\frac{4}{5}$
D) $e=\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{36}{100}}=\frac{4}{5}$