Question

Given the ellipse with equation $9x^2+25y^2=225$

Answer 1

${9x}^2+{25y}^2=225$

Dividing both sides by 225

$\frac{{9x}^2}{225}+\frac{{25y}^2}{225}=1$

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

Comparing with $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

$a=5,b=3(a>b)$

$e=\frac{4}{5}[b^2=a^2(1-e^2)]$

(A) Major axis $=2\times 5=10$

(B) Minor axis $=2\times 3=6$

(C) Focii $=(\pm ae,0)=(\pm \frac{4}{5}\times 5,0)=(\pm 4,0)$

(D) Vertices $=(\pm a,0)=(5,0)$