Question

The point $(1,1)$ lies ____________ the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$

• A. outside
• B. inside
• C. on the periphery
• D. on the auxillary circle

Answer 1

The correct option is B inside

We will substitute the given point in ellipse equation

$\Rightarrow$ $\frac{x^2}{4}+\frac{y^2}{9}-1$

$=\frac{1}{4}+\frac{1}{9}-1$

$\Rightarrow \frac{13}{36}-1$

$\Rightarrow \frac{-23}{36}<0$

By Substituting the point, we are getting less than $0$

$\therefore$ point lies inside the ellipse .