Find the Properties x^2+y^2=81

Problem

x2+y2=81

Solution

1. Identify the type of equation by comparing it to the standard form of a circle centered at the origin, which is x2+y2=r2

2. Determine the center of the circle by observing that there are no horizontal or vertical translations (h=0 and k=0.

3. Calculate the radius by taking the square root of the constant on the right side of the equation.

r2=81

√(,r2)=√(,81)

r=9

4. Find the diameter by doubling the radius.

d=2*r

d=2*(9)=18

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

x2+0=81

x=±9

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

0+y2=81

y=±9

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

Domain: *[−9,9]

Range: *[−9,9]

Final Answer

Center: *(0,0), Radius: *9, Diameter: *18, x-intercepts: *(±9,0), y-intercepts: *(0,±9)

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