Math Problem Statement
Write the standard form of the equation and the general form of the equation of the circle with the radius of 3 and the center (-3,0).
Solution
The equation of a circle is typically represented in two forms: standard form and general form.
1. Standard Form of the Equation of a Circle
The standard form is: where:
- is the center of the circle,
- is the radius.
For this problem:
- The center is ,
- The radius is .
Substituting these values into the standard form: Simplifying: So, the standard form of the equation is:
2. General Form of the Equation of a Circle
The general form is obtained by expanding the standard form and arranging it into:
Starting with the standard form , expand it: Now subtract 9 from both sides: So, the general form of the equation is:
Summary:
- Standard Form:
- General Form:
Would you like more details or have any questions?
Here are 5 related questions to explore:
- How do you find the center and radius from a circle's equation in general form?
- What is the equation of a circle with a radius of 5 and center at (2, -3)?
- How would the equation change if the radius doubled?
- How do you convert the general form of a circle to its standard form?
- How can you graph a circle from its standard form equation?
Tip: When converting between the standard and general forms of a circle, always complete the square if needed!
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Math Problem Analysis
Mathematical Concepts
Geometry
Equations of Circles
Formulas
Standard form of a circle: (x - h)^2 + (y - k)^2 = r^2
General form of a circle: Ax^2 + Ay^2 + Bx + Cy + D = 0
Theorems
Equation of a Circle
Suitable Grade Level
Grades 9-11
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