10 6 Equations of Circles Advanced Geometry What

What do you need to find the equation of a circle? • Coordinates of

Break it Down Given: Center is (h, k), the radius is r, and (x,

Standard Equation of a Circle (x – h)² + (y – k)² = r²

Example Write the standard equation of a circle that has a center at the

Example Write the standard equation of a circle with center (-5, 0) and radius

Example The point (2, 1) is on a circle whose center is (4, -3).

Example The point (0, -1) is on a circle whose center is ( -4,

Graphing The equation of a circle is (x + 2)² + (y – 3)²

Applying Graphs of Circles The equation of a circle is (x – 13)² +

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10. 6 Equations of Circles Advanced Geometry

What do you need to find the equation of a circle? • Coordinates of the Center of the circle. • Radius – Distance from center to a point on the circle

Let’s Look at a Circle

Break it Down Given: Center is (h, k), the radius is r, and (x, y) is a point on the circle. The distance between (x, y) and (h, k) is r… so let’s use the distance formula.

Break it Down •

Standard Equation of a Circle (x – h)² + (y – k)² = r² Where the center is at (h, k) & The radius is r

Example Write the standard equation of a circle that has a center at the origin and a radius of 5.

Example Write the standard equation of a circle with center (-5, 0) and radius 4. 8.

Example The point (2, 1) is on a circle whose center is (4, -3). Write the standard equation of the circle.

Example The point (0, -1) is on a circle whose center is ( -4, 1). Write the standard equation of the circle.

Graphing The equation of a circle is (x + 2)² + (y – 3)² = 9. First find the center and the radius of the circle, and then graph the circle.

Graphing Graph (x – 3)² + (y + 1)² = 4

Applying Graphs of Circles The equation of a circle is (x – 13)² + (y – 6)² = 9. Three points are located as follows: A(5, 6), B(14, 8), and C(20, 9). Which point is in the circle?