Question

Let $5x^2+7y^2=140$, then $(0,0)$ is:

• A. Inside the ellipse
• B. On the ellipse
• C. Outside the ellipse
• D. Centre of the ellipse

Answer 1

Answer: (A), (D)

The correct options are
A Inside the ellipse
D Centre of the ellipse

Equation of ellipse ${5x}^2+{7y}^2=140$

Dividing both sides by $140$

$\frac{x^2}{28}+\frac{y^2}{20}=1$

Comparing with $\frac{{(x-h)}^2}{a^2}+\frac{{(y-k)}^2}{b^2}=1$

$(h,k)=(0,0)$

Hence (0,0) is centre of given ellipse and it inside the ellipse.