Graph 9x^2+4y^2=36

Problem

9*x2+4*y2=36

Solution

1. Divide both sides of the equation by 36 to put the equation into the standard form of an ellipse.

(9*x2)/36+(4*y2)/36=36/36

2. Simplify the fractions to identify the denominators.

(x2)/4+(y2)/9=1

3. Identify the standard form (x2)/(b2)+(y2)/(a2)=1 for a vertical ellipse, where a2=9 and b2=4

a=3

b=2

4. Determine the center and the vertices. The center is at the origin (0,0) Since a is under the y term, the major axis is vertical.

Vertices: *(0,±3)

Co-vertices: *(±2,0)

5. Graph the ellipse by plotting the center (0,0) the vertices (0,3) and (0,−3) and the co-vertices (2,0) and (−2,0) then drawing a smooth curve through these points.

Final Answer

(x2)/4+(y2)/9=1

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