Maths-

General

Easy

Question

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

- 8
- 4
- 16
- none of these

Hint:

### The sum of the distances to any point on the ellipse (x,y) from the two foci (c,0) and (-c,0) is a constant. That constant will be 2a. If we let d_{1} and d_{2} bet the distances from the foci to the point, then **d**_{1} + d_{2} = 2a.

_{1}+ d

_{2}= 2a

## The correct answer is: 4

### Given :

Dividing both sides by 24, we get

The sum of the distances to any point on the ellipse (x,y) from the two foci (c,0) and (-c,0) is a constant. That constant will be 2a. If we let d1 and d2 bet the distances from the foci to the point, then d1 + d2 = 2a.

d1 + d2 = 2a

d1 + d2 = 2

d1 + d2 = 4

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

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