Find the Properties x^2+y^2=9

Problem

x2+y2=9

Solution

1. Identify the type of equation by comparing it to the standard form of a conic section. The equation x2+y2=r2 represents a circle centered at the origin.

2. Determine the center by observing that there are no horizontal or vertical shifts applied to x or y The center (h,k) is (0,0)

3. Find the radius by taking the square root of the constant on the right side of the equation. Since r2=9 the radius is r=√(,9)=3

4. Identify the intercepts by setting one variable to zero and solving for the other. Setting y=0 gives x=±3 (x-intercepts), and setting x=0 gives y=±3 (y-intercepts).

5. Determine the domain and range based on the center and the radius. The domain is [−3,3] and the range is [−3,3]

Final Answer

Center: *(0,0), Radius: *3, Domain: *[−3,3], Range: *[−3,3]

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