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Unit 5 Geometry

Unit 5 Geometry. 5.2 – Graph and write equations of circles. Georgia Performance standards. mm3G1a – Find equations of circles. MM3G1b – Graph a circle given an equation in general form. MM3G1c – Find the equation of a tangent line to a circle at a given point. . Vocabulary .

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Unit 5 Geometry

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  1. Unit 5 Geometry 5.2 – Graph and write equations of circles

  2. Georgia Performance standards • mm3G1a – Find equations of circles. • MM3G1b – Graph a circle given an equation in general form. • MM3G1c – Find the equation of a tangent line to a circle at a given point.

  3. Vocabulary • A circle is the set of all points (x,y) in a plane that are equidistant from a fixed point, called the center of the circle. The distance r between the center and any point (x,y) on the circle is the radius. The standard form of the equation of a circle with center at (0,0) and radius r

  4. Standard for of the equation of a parabola with vertex (0,0) is as follows: • Graph x2 = 25 – y2 • Steps: • Rewrite the equation • Identify the center and radius • Sketch the circle

  5. Standard for of the equation of a parabola with vertex (0,0) is as follows: • Graph x2 = 25 – y2

  6. Write an equation of a circle • The point (6,2) lies on a circle whose center is the origin. Write the standard form of the equation of the circle. • Steps: • Where is the origin? • How can we find the distance from the origin to the point? • Put in Standard Form • x2+y2 = r2

  7. Write an equation of a circle • The point (6,2) lies on a circle whose center is the origin. Write the standard form of the equation of the circle.

  8. Guided Practice: Page 180: 1-4 • Remember to Graph!! • Refer to your notes for help!!

  9. Find an equation of a line tangent to a circle • Find an equation of the line tangent to the circle x2 + y2 = 10 at (-1,3) • Some things that can help…. • A line tangent to a circle is perpendicular to the radius at the point of tangency • Slope formula: • Point slope formula: • How can you tell if a line is perpendicular? Negative Reciprocal

  10. Find an equation of a line tangent to a circle • Find an equation of the line tangent to the circle x2 + y2 = 10 at (-1,3)

  11. Write a circular model • A furniture store advertises free delivery up to a 50 mile radius from the store. If a customer lives 28 miles east and 41 miles north of the store, does the customer qualify for free delivery?

  12. Guided practice: Page 181: 5 & 6

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