Question

Let $5x^2+7y^2=140$, then $(3,-4)$ is:

• A. Outside the ellipse
• B. Inside the ellipse
• C. On the ellipse
• D. Data insufficient

Answer 1

The correct option is A Outside the ellipse

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

putting point $(3,-4)$ in equation of ellipse

$=5\times 3^2+7{(-4)}^2-140$

$=45+112-140$

$=17(>0)$

Hence, $(3,-4)$ is outside the ellipse.