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Algebra 2

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. What is a circle?. The set of all points equidistant from a given point.

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Algebra 2

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  1. Algebra 2 • Conic Sections: Circles and Parabolas

  2. 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

  3. 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 3

  4. P(x,y) C(5,1) Circles Start with the distance formula: Every circle has an equation of this form.

  5. Circles • Equation of a circle: • The circle with center ( h, k ) and radius r has the equation:

  6. Determine the center and the radius of the following circles: 1. x2 + (y - 2)2 = 25 2. (y + 3)2 + (x - 5)2 = 10

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

  8. Graph the previous circle

  9. 9-2 Circles What will the equation of a circle look like if the center is at the origin?

  10. 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.

  11. Given: x2 + y2 = 16 • Write an equation of a circle that is translated up 2 units. • Write an equation of a circle that is translated down 3 units and right 4. • Write an equation of a circle that is translated left 5 units, then reflected over the y-axis!

  12. 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? 12

  13. Exit Slip Time! • Homework: Day 1 on the assignment guide 13

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