Question

The sum of the distances of any point on the ellipse $3x^2+4y^2=24$ from its foci is :

• A. $8\sqrt{2}$
• B. $8$
• C. $16\sqrt{2}$
• D. $4\sqrt{2}$

Answer 1

Answer: (D)

$4\sqrt{2}$

Sum of the distances to any point on the ellipse

$(x,y)$ from the foci $(c,0)$ and $(-c,0)$ is $2a$.

${3x}^2+{4y}^2=24$

$\frac{x^2}{8}+\frac{y^2}{6}=1$ by comparing with $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

$a^2=8$

$a=2\sqrt{2}$

$\therefore$ Sum of distances $=2a=2\times 2\sqrt{2}$ $=4\sqrt{2}$