Question

Which are the foci of the ellipse represented by 25x² + 9y² = 225?

1) The foci are at (5, 0) and (-5, 0)
2) The foci are at (0, 5) and (0, -5)
3) The foci are at (3, 0) and (-3, 0)
4) The foci are at (0, 3) and (0, -3)

Answer 1

The foci of the ellipse represented by 25x² + 9y² = 225 are located at (3, 0) and (-3, 0).

Step-by-step explanation:

An ellipse is a closed curve such that the sum of the distances from a point on the curve to the two foci is constant. In the given equation, 25x² + 9y² = 225, we can rewrite it as x²/9 + y²/25 = 1. By comparing it with the standard form of the ellipse equation, a² + b² = 1, we can determine that a² = 9 and b² = 25. The foci of the ellipse can be calculated using the formula c = sqrt(a² - b²), where c is the distance from the center to each focus. In this case, the foci are at (3, 0) and (-3, 0).