Graph 16x^2+9y^2=144

Problem

16*x2+9*y2=144

Solution

1. Divide both sides of the equation by 144 to put the equation into the standard form of an ellipse.

(16*x2)/144+(9*y2)/144=144/144

2. Simplify the fractions to identify the denominators.

(x2)/9+(y2)/16=1

3. Identify the center and the values of a and b Since the equation is in the form (x2)/(b2)+(y2)/(a2)=1 the center is at (0,0)

a2=16⇒a=4

b2=9⇒b=3

4. Determine the vertices and co-vertices. Because a2 is under y2 the ellipse is vertical. The vertices are at (0,±4) and the co-vertices are at (±3,0)

5. Sketch the graph by plotting the center (0,0) the vertices on the y-axis, and the co-vertices on the x-axis, then drawing a smooth curve to connect them.

Final Answer

(x2)/3+(y2)/4=1

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