Math Problem Statement
What is the equation of the circle given r = sqrt(2) and center (h, k) = (0, 3)?
Solution
The image shows the equation for a circle, with the following key pieces of information:
- , representing the radius of the circle.
- , representing the center of the circle.
In general, the equation of a circle in standard form is:
Substituting the values given:
The equation of the circle becomes:
Simplifying:
This is the equation of the circle with radius and center at .
Would you like more details or have any questions?
Here are 5 related questions:
- How do you derive the equation of a circle from the general formula?
- What is the significance of the center in the equation of a circle?
- How would you graph the circle ?
- What happens if the radius is increased or decreased in the equation of a circle?
- Can you describe how to find the area of the circle given the radius ?
Tip: Always remember to square the radius when using it in the equation of a circle.
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Math Problem Analysis
Mathematical Concepts
Geometry
Equations of Circles
Formulas
(x - h)^2 + (y - k)^2 = r^2
Theorems
Equation of a Circle
Suitable Grade Level
Grades 9-11