Which equation represents the graph?

The equation represents the graph is (y+1)² / 9 + (x+3)²/1 = 1 i.e, option(a)

Define Ellipse

In mathematics, an ellipse is the location of points in a plane so that their separation from a fixed point has a fixed ratio of "e" to their separation from a fixed line (less than 1). The conic section, which is the intersection of a cone with a plane that does not intersect the base of the cone, includes the ellipse. The eccentricity of the ellipse is symbolized by the constant ratio "e," the fixed point is known as the focus, and the fixed line is known as the directrix (d).

Standard from of the equation of an ellipse with centre (0,0) and major axis on x-axis is,

x² / a² + y² / b² = 1

Standard from of the equation of an ellipse with centre (H, K) and major axis parallel to the x-axis is,

(x - h)² / a² + (y - k)² / b² = 1

In equation,

(y+1)² / 9 + (x+3)²/1 = 1

Ellipse properties are :  (h,k) = (-3, -1) , a = 3, b = 1

b>a therefore b is semi-major axis, a is semi minor axis.

Ellipse Centre are :  (h,k) = (-3, -1) , a = 1, b = 3

Hence, the equation represents the graph is (y+1)² / 9 + (x+3)²/1 = 1 i.e, option(a).

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Answer:

Step-by-step explanation: 9x3

9x2

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