Circles in the Coordinate Plane I can identify and understand equations for circles.

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Circles in the Coordinate Plane I can identify and understand equations for circles.

X^2 + y^2 = r^2 ► If the circle is in the middle of the coordinate plane, (0,0) then the formula for it is x^2 + y^2 = r^2

(y – 4)^2 – (x - 4)^2 = r^2 If it is not in 0,0, and instead on 4,4, then The formula would look like this: If it is not in 0,0, and instead on 4,4, then The formula would look like this: (y – 4)^2 – (x - 4)^2 = r^2 (y – 4)^2 – (x - 4)^2 = r^2

Where Does the Circle Formula Come From? Using the distance formula, the radius of the circle is represented by: Using the distance formula, the radius of the circle is represented by: = Equation of a circle h and k are the x and y coordinates in the center of the circle.

Example 1 Write the equation for the circle with center at (3,-5) and a radius of 3. Write the equation for the circle with center at (3,-5) and a radius of 3.

Answer Notice how the coordinate of -5 appears as (y+5)^2.

Example 2 Given the equation of the circle (x + 3)^2 + (y – 6)^2 = 24, what are the coordinates of the center and the radius.

Answer The center is (-3,6) and the radius is 24 = 2 6