Graph 6x^2+6y^2=144

Problem

6*x2+6*y2=144

Solution

1. Identify the type of conic section by observing that both x2 and y2 have the same positive coefficient. This indicates the equation represents a circle.

2. Divide both sides of the equation by 6 to transform it into the standard form of a circle equation, x2+y2=r2

x2+y2=144/6

x2+y2=24

3. Determine the center of the circle. Since there are no horizontal or vertical shifts (no h or k values subtracted from x or y, the center is at the origin.

Center=(0,0)

4. Calculate the radius r by taking the square root of the constant on the right side.

r2=24

r=√(,24)

r=2√(,6)

5. Approximate the radius for graphing purposes.

r≈4.9

6. Graph the circle by plotting the center at (0,0) and drawing a curve that maintains a distance of approximately 4.9 units from the center in all directions. Key points include (0,±4.9) and (±4.9,0)

Final Answer

6*x2+6*y2=144⇒x2+y2=24

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