Question

The position of the point $(1,2)$ relative to the ellipse $2x^2+7y^2=20$ is

• A. outside the ellipse
• B. inside the ellipse but not at the focus
• C. on the ellipse
• D. at the focus

Answer 1

The correct option is A outside the ellipse

$f(x,y)={2x}^2+7y^2-20$

Point will be outside of ellipse if $f(1,2)>0$

on ellipse if $f(1,2)=0$

will be inside if $f(1,2)<0$

$f(1,2)={2\times 1}^2+7{\times 2}^2-20=10$

Here we see that $f(1,2)>0$ so point will be outside of ellipse

So correct answer will be option A