Question

Foci of the Ellipse $25x^2+9y^2-150x-90y+225$ = 0 are

• A. (3,9) (3,1)
• B. (4,9) (4,1)
• C. (5,7) (4,7)
• D. (6,9) (5,1)

Answer 1

The correct option is A

(3,9) (3,1)

$25x^2+9y^2-150x-90y+225$ = 0

$25(x^2-6x)+9(y^2-10y)$ = -225

$25(x-3{)}^2+9(y-5{)}^2$=225 $\Rightarrow$ $\frac{(x-3{)}^2}{9}+\frac{(y-5{)}^2}{25}$ = 1

e = $\frac{4}{5}$, S = (h, k$\pm$be) = (3,5$\pm$4) = (3,9) and (3,1)