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# CCGPS Geometry - PowerPoint PPT Presentation

CCGPS Geometry. 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. EOCT Practice Question.

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CCGPS Geometry

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### CCGPS Geometry

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

### EOCT Practice Question

• Use the Quadratic formula to find the solutions to the following quadratic equation:

• a.)c.)

• b.)d.)

### Circle:

• What are the coordinates of this circle’s center?

## 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 **

### Finding the Equation of a Circle

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.

### Writing Equations of Circles

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

### Writing Equations of Circles

Write the standard equation of the circle:

(x – 2)2 + (y + 9)2 = 11

### Equation of a Circle

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

### Graphing Circles

(x – 3)2 + (y – 2)2 = 9

Center (3, 2)

### Graphing Circles

(x + 4)2 + (y – 1)2 = 25

Center (-4, 1)

### Graphing Circles

(x – 5)2 + y2 = 36

Center (5, 0)

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.

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