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

0 votes

2x^2 + 6y^2 = 12

asked Jul 11, 2013 in PRECALCULUS by angel12 Scholar

2 Answers

0 votes

The given equation of ellipse is
 

image

The standard form of the equation of an ellipse is

image

image

Divide both sides with 12

image

image

image

image

Therefore c=2

image

The center at ( h, k) ⇒( 0,0)

image

image

image

image

image

 

image

The solution is centre (0,0) and

image

image

.

 

answered Jul 11, 2013 by jouis Apprentice

Vertices  of image are  image

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

0 votes

The ellipse equation image

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.

image

image

image

image

Compare it to standard form of ellipse image

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

= length of semi-minor axis

image

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

Vertices are image

is the distance from the center to each focus.

image

image

image

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

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

answered Jun 5, 2014 by david Expert

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