Question

The foci of the ellipse, $25(x+1{)}^2+9(y+2{)}^2=225$ are

• A. $(-1,2)$ and $(-1,-6)$
• B. $(-2,1)$ and $(-2,6)$
• C. $(-1,-2)$ and $(-2,-1)$
• D. $(-1,-2)$ and $(-1,-6)$

Answer 1

The correct option is A $(-1,2)$ and $(-1,-6)$

$25(x+1{)}^2+9(y+2{)}^2=225$
$\Rightarrow \frac{(x+1{)}^2}{9}+\frac{(y+2{)}^2}{25}=1$
Centre is at $(-1,-2)$
$a=3,b=5,$
$b>a\Rightarrow$ vertical ellipse
$\because a^2=b^2(1-e^2)$
$\Rightarrow e^2=1-\frac{a^2}{b^2}$
$e=\frac{4}{5}$
So, $be=4$
Foci will be $(-1,-2\pm be)$
$\equiv (-1,-2\pm 4)$
$\equiv (-1,-6)$ and $(-1,2)$