Math Problem Statement
Find the equation of the circle shown. Write the equation in center-radius (or standard) form.
Solution
To find the equation of the circle, we need the following pieces of information from the graph:
- Center of the circle (h, k): The center can be identified as the point around which the circle is symmetric.
- Radius (r): This is the distance from the center to any point on the circle.
From the image:
- The center of the circle appears to be at .
- The radius can be observed as the distance from the center to the point where the circle crosses the x-axis at , so the radius .
The general equation of a circle in center-radius form is:
Substituting the values , , and :
So, the equation of the circle is:
Would you like more details or have any other questions?
Here are 5 related questions you can explore:
- How do we derive the center-radius form of a circle's equation?
- What is the relationship between the general form and the center-radius form of a circle's equation?
- How can we find the radius from the diameter or the circumference?
- Can this equation be converted into the general form of a circle equation?
- How can you determine the equation of a circle given three points on the circle?
Tip: Always double-check the coordinates of the center and the radius by counting grid squares carefully to ensure accuracy in reading the graph!
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Math Problem Analysis
Mathematical Concepts
Geometry
Circles
Coordinate Geometry
Formulas
Equation of a circle: (x - h)^2 + (y - k)^2 = r^2
Theorems
Circle Equation Theorem
Suitable Grade Level
Grades 8-10