Graph (x^2)/36+(y^2)/20=1

Problem

(x2)/36+(y2)/20=1

Solution

1. Identify the type of conic section. Since the equation is in the form (x2)/(a2)+(y2)/(b2)=1 with positive denominators, it is an ellipse centered at the origin (0,0)

2. Determine the lengths of the semi-axes. Here a2=36 and b2=20 Taking the square roots gives a=6 and b=√(,20)=2√(,5)≈4.47

3. Locate the vertices and co-vertices. Since a>b the major axis is horizontal. The vertices are at (±6,0) and the co-vertices are at (0,±2√(,5))

4. Calculate the foci using the formula c2=a2−b2

c2=36−20

c2=16

c=4

The foci are located at (±4,0)

5. Sketch the graph by plotting the center (0,0) the vertices (±6,0) and the co-vertices (0,±4.47) then drawing a smooth curve through these points.

Final Answer

(x2)/36+(y2)/20=1* is an ellipse with vertices *(±6,0)* and co-vertices *(0,±2√(,5))

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