What are the foci of the ellipse given by the equation 25x² + 16y² = 400

Solution:

The equation of the ellipse is 25x² + 16y² = 400

Dividing the equation by 400 throughout we get:

⇒ 25x² + 16y² = 400

⇒ 25x²/400 + 16y²/400 = 400/400

⇒ x²/16 + y²/25 = 1

The above equation of the form:

x²/b² + y²/a² = 1(a > b)

Therefore center to focus distance:

c = √a² - b²

= √(25 - 16)

= √9

= 3

The Foci: (0, ±3)

The foci of the ellipse are (0, +3) and (0, -3)

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What are the foci of the ellipse given by the equation 25x² + 16y² = 400

Summary:

The foci of the ellipse given by the equation 25x² + 16y² = 400 are (0, +3) and (0, -3)