Question

The foci of the conic section
$25x^2+16y^2-150x=175$ are

• A. $(0,\pm 3)$
• B. $(0,\pm 2)$
• C. $(3,\pm 3)$
• D. $(0,\pm 1)$

Answer 1

The correct option is C $(3,\pm 3)$

$25x^2+16y^2-150x=175{\left(5x\right)}^2-150x+{\left(15\right)}^2+16y^2=175+{\left(15\right)}^2{(5x-15)}^2+16y^2=40025{(x-3)}^2+16y^2=400\frac{{(x-3)}^2}{16}+\frac{y^2}{25}=1$

Major axis of the ellipse is $y$ axis

So $a=5,b=4$

$e^2=1-\frac{b^2}{a^2}=1-\frac{16}{25}=\frac{9}{25}\Rightarrow e=\frac{3}{5}$

Coordinates of foci of standard ellipse with major axis as $y$ are $(0,\pm ae)$

$\Rightarrow$ foci of given ellipse is

$(3,\pm 5\times \frac{3}{5})(3,\pm 3)$'

So opttion $C$ is correct