Algebra 2

Conic Sections: Circles and Parabolas

Circles

I can learn the relationship between the center and radius of a circle and the equation of a circle.

I can graph circles I can write equations of circles

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What is a circle?

The set of all points equidistant from a given point.

That given point: center That distance: radius

Other terms: diameter, circumference, area

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Circles

C(5,1)

P(x,y)

Start with the distance formula:

Every circle has an equation of this form.

Circles

Equation of a circle:

The circle with center ( h, k ) and radius r has the equation:

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Determine the center and the radius of the following circles:

1. x2 + (y - 2)2 = 25

2. (y + 3)2 + (x - 5)2 = 10

Circles

What is the equation of a circle with center ( -4, 3 ) and radius 5?

Graph the previous circle

9-2 Circles

What will the equation of a circle look like if the center is at the origin?

Circles

Check out this website to see how the equation affects the position of a circle:

http://www.shodor.org/interactivate/activities/ConicFlyer/?version=1.6.0_13&browser=Mozilla&vendor=Sun_Microsystems_Inc.

Given: x2 + y2 = 16

1. Write an equation of a circle that is translated up 2 units.

2. Write an equation of a circle that is translated down 3 units and right 4.

3. Write an equation of a circle that is translated left 5 units, then reflected over the y-axis!

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Tangent to a Circle

a line that intersects a circle at one point.

Can you write and equation of a circle that has a center of (5, -1) and is tangent to the line x = 8?

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Exit Slip Time!

Homework: Day 1 on the assignment guide

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