Question

What is the equation of the following graph?

	A.
	B.
	C.
	D.

 

Answer 1

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.