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Your Notes Checkpoint Graph the equation. Identify the radius. 1. x2 5 4 2 y2 r 5 2 Example 2 Write an equation of a circle The point (23, 4) lies on a circle whose center is the origin. Write the standard form of the equation of the circle. The circle’s radius r must be the distance between the center and (23, 4). Use the distance formula. r 5 Ï }}} ( 23 2 0 ) 2 1 ( 4 2 0 ) 2 5 Ï } 9 1 16 5 Ï } 25 5 5 Use the standard form with r 5 5 to write an equation of the circle. x2 1 y2 5 r2 Standard form x2 1 y2 5 5 2 Substitute for r. x2 1 y2 5 25 Simplify. Example 3 Find a tangent line Write an equation of the line tangent to the circle x2 1 y2 5 17 at (4, 21). A line tangent to a circle and the radius to the point of tangency are perpendicular. The radius with endpoint 21 2 0 1 (4, 21) has slope m 5 } 5 2 } , so the slope 4 2 0 4 of the tangent line at (4, 21) is the negative reciprocal of 2 1 } , or 4 . An equation of the tangent line is as 4 follows: y 1 1 5 4 (x 2 4 ) Point-slope form y 5 4x 2 17 Solve for y. Copyright © Holt McDougal. All rights reserved. Lesson 9.3 Algebra 2 Notetaking Guide 239 1 y 1 x
Your Notes Homework Example 4 Write a circular model Lighthouse The beam from Oak Island Lighthouse in North Carolina can be seen for up to 24 miles. You are 18 miles east and 9 miles south of the lighthouse. Can you see the lighthouse beam? Solution 1. Write an inequality for the region lit by the beam. This region is all the points that satisfy the following inequality: x2 1 y2 < 2 2. Substitute the coordinates (18, 9) into the inequality. x 2 1 y 2 < 2 Inequality < 2 Substitute for x and y. The inequality is . You see the lighthouse beam. Checkpoint Complete the following exercises. 2. Write the standard form of the equation of the circle with center at the origin that passes through the point (6, 23). 3. Write an equation of the line tangent to the circle x 2 1 y 2 5 34 at (23, 25). 4. From Example 4, suppose you are 16 miles east and 19 miles south of the lighthouse. Can you see the lighthouse beam? 240 Lesson 9.3 Algebra 2 Notetaking Guide Copyright © Holt McDougal. All rights reserved.
Page 1 and 2: Your Notes 9.1 Apply the Distance a
Page 3 and 4: Your Notes Checkpoint Complete the
Page 5 and 6: Your Notes Homework Example 4 Find
Page 7 and 8: Your Notes 9.2 Graph and Write Equa
Page 9 and 10: Your Notes Example 1 Graph an equat
Page 11 and 12: Your Notes Homework Example 2 Write
Page 15: Your Notes Checkpoint Graph the equ
Page 23 and 24: Your Notes Homework Example 3 Write
Page 29 and 30: Your Notes Example 2 Write an equat
Page 31 and 32: Your Notes Homework Example 3 Solve
Page 33 and 34: Your Notes 9.6 Translate and Classi
Page 35 and 36: Your Notes Example 1 Graph the equa
Page 37 and 38: Your Notes Write an equation of the
Page 39 and 40: Your Notes Example 4 Write an equat
Page 41 and 42: Your Notes Homework CLASSIFYING CON
Page 43 and 44: Your Notes 9.7 Solve Quadratic Syst
Page 45 and 46: Your Notes Example 2 Solve a linear
Page 47 and 48: Your Notes Example 3 Solve a quadra
Page 49 and 50: Your Notes Homework Example 4 Solve
Page 51 and 52: Focus On Graphing Use after Lesson
Page 53 and 54: Your Notes Homework Example 2 Use e
Page 55 and 56: Words to Review Give an example of
Page 57 and 58: Co-vertices Hyperbola 2 Conic secti

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