6-2 Conic Sections: Circles Geometric definition: A circle is formed by cutting a circular cone with a plane perpendicular to the symmetry axis of the.

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Presentation transcript:

6-2 Conic Sections: Circles Geometric definition: A circle is formed by cutting a circular cone with a plane perpendicular to the symmetry axis of the cone. This intersection is a closed curve, and the intersection is parallel to the plane generating the circle of the cone. Algebraic definition: A circle is the set of all points that are equally distant from a fixed point (the center).

y x (h,k) (x,y) r Center-Radius Form Example 1: Find the center and radius:

Example 2: Find the center and radius: Example 3: Find the center and radius: Example 4: Find the center and radius:

Example 5: Write the equation of a circle centered at (2,  7) and having a radius of 5.

Step 1: Write in center-radius form: Step 2: Check that P(3, 5) lies on the rim of the circle: Step 3: Identify the center and radius:

Step 1: Solve the linear equation for one variable: Step 2: Substitute into variable of circle equation: Step 3: Substitute single-variable solutions into linear equation to solve for corresponding values: