ellipses 4

Question

Find the center, vertices, and foci of the ellipse with equation 3x² + 6y² = 18

Answer 1

The equation of ellipse is 3x² +6y² = 18.

Divide each side by 18.

3x²/18 +6y² /18 = 18/18.

x² /6+y² /3= 1.         (a>b)

Compare the equation (x - 0)²/6 + (y - 0)²/3 = 1 with (x - h)²/b² + (y - k)²/a² = 1.

b² = 3, a² = 6, h = 0 and k = 0.

b = √3 and a = √6.

To find the value of c, substitute the value of a² = 6 and b² = 3 in c² = a² - b².

c² = 6 -3

c² =3

c = ± √3.

Center = (h, k ) = (0, 0).

Foci = (h, k ± c) = (0, 0 ± √3) = (0, √3) and (0, -√3).

vertices  = (h, k ± a) = (0, 0 ± √6) = (0, √6) and (0, -√6).