Math Problem Statement
If the circle has the center of -2 and +2 and as the radius of 3 what is the standard form and the general form of it
Solution
Solution
Standard Form of the Circle's Equation:
The equation of a circle in standard form is:
Where:
- is the center of the circle.
- is the radius.
Given:
- Center : , .
- Radius .
Substitute the values:
Thus, the standard form is:
General Form of the Circle's Equation:
To convert the standard form to the general form, expand and simplify:
Expand each term:
Combine like terms:
Simplify:
Thus, the general form is:
Final Answer:
- Standard Form:
- General Form:
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Related Questions:
- What are the properties of a circle represented in general form?
- How do you find the radius and center from the general form of a circle?
- What are the steps to graph a circle using the standard form equation?
- How do transformations of a circle affect its standard form equation?
- Can a circle have a radius of zero? If so, what would its equation look like?
Tip:
Always verify the center and radius when switching between standard and general forms to avoid calculation errors.
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Math Problem Analysis
Mathematical Concepts
Geometry
Equations of a Circle
Formulas
Standard form of a circle: (x - h)^2 + (y - k)^2 = r^2
General form of a circle: x^2 + y^2 + Dx + Ey + F = 0
Theorems
Definition of a Circle
Suitable Grade Level
Grades 9-12