Find the center, vertices, and foci of the ellipse with equation

Question

2x^2 + 6y^2 = 12

Answer 1

The given equation of ellipse is
 

The standard form of the equation of an ellipse is

Divide both sides with 12

Therefore c=2

The center at ( h, k) ⇒( 0,0)

 

The solution is centre (0,0) and

.

 

Comments

Vertices  of are 

Foci: (2, 0), (-2, 0).

Answer 2

The ellipse equation

The standard form for an ellipse is in a form = 1, So divide both sides of equation by 12 to set it equal to 1.

Compare it to standard form of ellipse

a ² > b ²

If the larger denominator is under the "x " term, then the ellipse is horizontal.

center (h, k ) = (0, 0)

a  = length of semi-major axis

b  = length of semi-minor axis

Vertices: (h + a, k ), (h - a, k )

Vertices are

c  is the distance from the center to each focus.

Foci: (h + c , k ), (h - c , k )

Foci: (2, 0), (-2, 0).