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

Question

The sum of the distances of any point on the ellipse 3x2+4y2=24 from its foci, is: (A)  8√2  (B) 8 (C)  16√2  (D)  2√2

Tardigrade Admin · Accepted Answer

Equation of ellipse is 3x2+4y2=24 ⇒ (x2/8)+(y2/6)=1 Here a=2√2 and b=√6 . The sum of the distances of any point on the ellipse from its foci is 2a=4√2 .

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

$82$

8

$162$

$22$

$42$

Equation of ellipse is $3 x^{2} + 4 y^{2} = 24$ $\Rightarrow$ $\frac{x ^{2}}{8} + \frac{y ^{2}}{6} = 1$ Here $a = 22$ and $b = 6$ . The sum of the distances of any point on the ellipse from its foci is $2 a = 42$ .

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

82​

8

162​

22​

42​