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

Problem

4*x2+9*y2=36

Solution

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

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

2. Simplify the fractions to identify the denominators.

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

3. Identify the standard form (x2)/(a2)+(y2)/(b2)=1 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>b the major axis is horizontal. The vertices are at (±3,0) and the co-vertices are at (0,±2)

5. Sketch the graph by plotting the center (0,0) the vertices (3,0) and (−3,0) and the co-vertices (0,2) and (0,−2) then drawing a smooth oval connecting these points.

Final Answer

(x2)/3+(y2)/2=1

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