Find the center, vertices, and foci of the ellipse with equation 3x2 + 8y2 = 24

Centre: (0,0)

Vertices: (2sqrt (2), 0) (-2sqrt (2), 0)

Co-vertices: (0, sqrt (3)) (0, - sqrt (3))

Foci: (sqrt (5), 0) (-sqrt (5), 0)

Step-by-step explanation:

(x - h) ²/a² + (y - k) ²/b² = 1

3x²/24 + 8y²/24 = 1

x²/8 + y²/3 = 1

Centre: (0,0)

Vertices:

y² = 3

y = + / - sqrt (3)

(0, sqrt (3))

(0, - sqrt (3))

x² = 8

x = + / - sqrt (8) = + / - 2sqrt (2)

(2sqrt (2), 0)

(-2sqrt (2), 0)

Foci: (c, 0)

c² = a² - b²

c² = 8 - 3 = 5

c = + / - sqrt (5)

The center is at (0,0)

The vertices are at ((±2 sqrt (2),0)

foci are (±sqrt (5),0)

Step-by-step explanation:

3x^2 + 8y^2 = 24

Divide each side by 24

3x^2 / 24 + 8y^2/24 = 24/24

x^2/8 + y^2 / 3 = 1

The general equation of an ellipse is

(x-h) ^2 / a^2 + (y-k) ^2 / b^2 = 1

a>b (h, k) is the center

the coordinates of the vertices are (±a, 0)

the coordinates of the foci are (±c, 0), where ^c2=a^2-b^ 2

The center is at (0,0)

a = sqrt (8) = 2sqrt (2)

The vertices are at ((±2 sqrt (2),0)

c = 8 - 3 = 5

foci are (±sqrt (5),0)