Find the Properties x^2+y^2=4

Problem

x^2+y^2=4

Solution

1. Identify the type of equation by comparing it to the standard form of a circle centered at the origin, which is x^2+y^2=r^2

2. Determine the center of the circle by observing that there are no horizontal or vertical shifts (no h or k values subtracted from x or y.

3. Calculate the radius by taking the square root of the constant on the right side of the equation, where r^2=4

4. Find the diameter by multiplying the radius by 2

5. Determine the xintercepts by setting y=0 and solving for x

6. Determine the yintercepts by setting x=0 and solving for y

7. State the domain and range based on the center and the radius.

Final Answer

Shape: Circle

Center: *(0,0)

Radius: *2

Diameter: *4

x-intercepts: *(2,0),(−2,0)

y-intercepts: *(0,2),(0,−2)

Domain: *[−2,2]

Range: *[−2,2]

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