Question

The equation of the ellipse whose vertices are ( ±5,0) and foci are ( ± 4 , 0 ) is

• A. $25x^2+9y^2=225.$
• B. $9x^2+25y^2=225.$
• C. $3x^2+4y^2=192.$
• D. None of these

Answer 1

The correct option is B

$9x^2+25y^2=225.$

Vertices ( ± 5 , 0) $\equiv (\pm a,0)\Rightarrow a=5$

Foci ( ±4,0) $\equiv (\pm ae,0)\Rightarrow e=\frac{4}{5},\therefore b=\left(5\right)\left(\frac{3}{5}\right)=3$

Hence, the equation is $\frac{x^2}{25}+\frac{y^2}{9}=1$ ie., $9x^2+25y^2=225.$