Question

If for the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,S_1=\frac{x_1^2}{a^2}+\frac{y_1^2}{b^2}-1$, for point $(x_1,y_1)$, Which of the following is true

• A. $S_1=0\Rightarrow (x_1,y_1)$ is on the ellipse
• B. $S_1$$>0$$\Rightarrow (x_1,y_1)$ is inside the ellipse
• C. $S_1$$<0$$\Rightarrow (x_1,y_1)$is outside the ellipse
• D. $S_1$$>0$$\Rightarrow (x_1,y_1)$ is outside the ellipse

Answer 1

Answer: (A), (D)

The correct options are
A $S_1=0\Rightarrow (x_1,y_1)$ is on the ellipse
D $S_1$$>0$$\Rightarrow (x_1,y_1)$ is outside the ellipse

It's important to remember the fact that
If $S_1=0$, $(x_1,y_1)$ is on the ellipse
$S_1$$<0$, $(x_1,y_1)$ is inside the ellipse
$S_1$$>0$, $(x_1,y_1)$ is outside the ellipse
$\therefore$ options a, d are correct.