Math Problem Statement
Write the standard equation of a circle whose center
Solution
The image shows a handwritten problem asking to "Write the standard equation of the circle whose center is at and passes through the point ."
Solution:
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Identify the center and a point on the circle:
- Center
- Point on the circle
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Formula for the standard equation of a circle: where is the radius.
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Find the radius: The radius is the distance between the center and the given point , calculated by: Substituting the given values:
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Write the equation: Substitute , , and into the standard equation of the circle: Simplifying this:
Final Answer:
The standard equation of the circle is:
Would you like more details or have any questions?
Related Questions:
- What is the general form of a circle's equation?
- How do you find the radius if only the diameter is given?
- What are the steps to convert the general form to the standard form of a circle's equation?
- How can you find the center and radius from the general form of a circle's equation?
- What is the equation of a circle if its diameter endpoints are given?
- How does changing the center coordinates affect the circle's equation?
- How do you find the equation of a circle if it is tangent to the x-axis?
- How do you determine if a point lies inside, on, or outside a given circle?
Tip:
When given the center and a point on a circle, always start by finding the radius using the distance formula before substituting into the standard circle equation.
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Math Problem Analysis
Mathematical Concepts
Geometry
Circle Equations
Formulas
Distance Formula
Standard Equation of a Circle
Theorems
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Suitable Grade Level
Grades 9-12
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