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CCGPS Geometry

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UNIT QUESTION: How are the equations of circles and parabolas derived?

Standard: MCC9-12..A.REI.7, G.GPE.1,2 and 4

Today’s Question:

How is the equation of a circle derived?

Standard: MCC9-12..G.GPE.1

- Use the Quadratic formula to find the solutions to the following quadratic equation:
- a.)c.)
- b.)d.)

- What are the coordinates of this circle’s center?
- What is its radius?

Equations of Circles

Standard Form of a Circle

Circle with center at the origin (0,0)

Standard form of a circle that is translated

**Center: (h, k) Radius: r **

Write the standard form of the equation for the circle that has a center at the origin and has the given radius.

1.r = 92.r = 143.

Write the standard equation of the circle:

Center (4, 7) Radius of 5

(x – 4)2 + (y – 7)2 = 25

Writing Equations of Circles

Write the standard equation of the circle:

Center (-3, 8) Radius of 6.2

(x + 3)2 + (y – 8)2 = 38.44

Write the standard equation of the circle:

Center (2, -9) Radius of

(x – 2)2 + (y + 9)2 = 11

The center of a circle is given by (h, k).

The radius of a circle is given by r.

The equation of a circle in standard form is

(x – h)2 + (y – k)2 = r2

(x – 3)2 + (y – 2)2 = 9

Center (3, 2)

Radius of 3

(x + 4)2 + (y – 1)2 = 25

Center (-4, 1)

Radius of 5

(x – 5)2 + y2 = 36

Center (5, 0)

Radius of 6

To write the standard equation of a translated circle, you may need to complete the square.

Graphing a circle in Standard Form!!

Example:

Standard Form!!

Center: (4, 0) r: 3

Write the standard equation for the circle. State the center and radius.