Question

For each point $(x,y)$ on the ellipse with centre at the origin and principal axes along the coordinate axes, the sum of the distances from the point $(x,y)$ to the points $(\pm 2,0)$ is 8 . The positive value of $x$ such that $(x,3)$ lies on the ellipse, is

• A. $\frac{\sqrt{3}}{3}$
• B. 2
• C. 4
• D. $2\sqrt{3}$

Answer 1

Answer: (B)

$c=2;a=4$
equation of the ellipse is
$\left(\frac{x^2}{a^2}+\frac{y^2}{a^2-c^2}=1\right)$
$\frac{x^2}{16}+\frac{y^2}{16-4}=1\Rightarrow \frac{x^2}{16}+\frac{y^2}{12}=1$
when $y=3$ then $\frac{x^2}{16}+\frac{9}{12}=1\Rightarrow \frac{x^2}{16}=\frac{1}{4}\Rightarrow x=2$