Question

The equation of an ellipse is given in its standard form as $16x^2+y^2=16$, then coordinates of the foci are,

• A. $(0,+\sqrt{15})$
• B. $(0,-\sqrt{15})$
• C. Both (A) and (B)
• D. None of these

Answer 1

The correct option is C Both (A) and (B)

The ellipse is, $16x^2+y^2=16$.

Major axis is along Y-axis.

Dividing both sides by $16$.

$\frac{x^2}{1}+\frac{y^2}{16}=1$

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

$\therefore a^2=1and{b}^2=16$

$\therefore a=1andb=4(b>a)$

$\therefore c=\sqrt{b^2-a^2}⟹c=\sqrt{15}$

foci are $(0,\pm \sqrt{15})$.

Hence option ${}^{\prime }{C}^{\prime }$ is the answer.