Math Problem Statement
Solution
To find the equation of a circle centered at the origin and passing through the point , we can use the standard form of a circle equation:
Since the circle passes through , the radius is the distance from the origin to this point, which is .
Thus, the equation of the circle is:
Simplifying, we get:
Would you like a detailed explanation? Here are some related questions:
- What is the general equation for a circle centered at any point ?
- How do you find the radius of a circle when given two points on its diameter?
- What if the circle passed through a different point, like ?
- Can this method be used for circles not centered at the origin?
- How do you graph a circle equation?
Tip: Always check if the point given is on the circle by substituting it into the equation.
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Math Problem Analysis
Mathematical Concepts
Geometry
Circles
Equation of a Circle
Formulas
x^2 + y^2 = r^2
Theorems
Distance Formula
Suitable Grade Level
Grades 9-10
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