Question

The sum of the distances of any point on the ellipse 3x2 + 4y2 = 24 from its foci is​

Answer 1

Answer:

The sum of the focal distances of any point on the from its focus is

$4\sqrt{2}$

Step-by-step explanation:

$\textbf{Focal property of ellipse:}$

$\textit{The sum of the focal distances of any point}$

$\textit{on the ellipse is equal to the length }$

$\textit{of the major axis}$

$\text{Given:}$

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

$\text{divide both sides by 24, we get}$

$\frac{x^2}{8}+\frac{y^2}{6}=1$

$\text{comparing with \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 we get}$

$a^2=8\:,b^2=6$

$\implies\,a=2\sqrt{2}$

$\textbf{By focal property,}$

$\text{The sum of the distances of any point on the ellipse from its focus is 2a}$

$=2*2\sqrt{2}$

$\bf=4\sqrt{2}$