Question

Point $(1,2)$ lies _____ the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$.

• A. inside
• B. outside
• C. on
• D. None of the above

Answer 1

The correct option is A inside

The region (disk) bounded by the ellipse is given by the equation:

$\frac{(x-h{)}^2}{a^2}+\frac{(y-k{)}^2}{b^2}\le 1$ centered at $(h,k)$ ..... $\left(1\right)$

Point $(x,y)$ lies inside the ellipse if it satisfies $\left(1\right)$

Take $(x,y)=(1,2)$

Consider, $\frac{(x-0{)}^2}{16}+\frac{(y-0{)}^2}{9}$

$=\frac{1^2}{16}+\frac{2^2}{9}=\frac{73}{144}<1$

Hence, $(1,2)$ lies inside the given ellipse.