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What is the equation of the following graph?

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What is the equation of the following graph?
ellipse through the points (5, 2), (2, 4), (negative 1, 2) and (2, 0)
A. x minus 2 squared divided by 4 plus y minus 2 squared divided by 9 equals 1
B. x minus 2 squared divided by 9 minus y minus 2 squared divided by 4 equals 1
C. x plus 2 squared divided by 9 plus y plus 2 squared divided by 4 equals 1
D. x minus 2 squared divided by 9 plus y minus 2 squared divided by 4 equals 1

 

asked Sep 8, 2014 in ALGEBRA 2 by tonymate Pupil

1 Answer

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Best answer

From the graph, the ellipse is horizontal.

The major axis : 2a = 6 ----> a = 3.

The minor axis : 2b = 4 ----> b = 2.

Vertices : (- 1, 2) and (5, 2)

Co-vertices : (2, 0) and (2, 4)

Center = The mid point of the vertices or co-vertices.

(h, k) = [(2 + 2)/4, (0 + 4)/2]

(h, k) = (2, 2)

Horizontal ellipse with center (h, k) : (x - h)2/a2 + (y - k)2/b2 = 1

Substitute a = 3, b = 2 and (h , k) = (2, 2) in the Horizontal ellipse.

(x - 2)2/32 + (y - 2)2/22 = 1

(x - 2)2/9 + (y - 2)2/4 = 1

The option D is correct.

answered Sep 8, 2014 by casacop Expert
selected Sep 8, 2014 by tonymate

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