Assignment Assignment for Lesson.1 Name Date Conics? Conics as Cross Sections Determine the conic section that results from the intersection of the double-napped cone shown and each plane described. 1. A plane that passes through one nappe of the double-napped cone and is perpendicular to the axis of the cone The intersection is a. 2. A plane that passes through one nappe of the double-napped cone and is parallel to the edge of the cone 30 The intersection is a. 3. A plane that passes through both nappes of the double-napped cone and is parallel to the axis of the cone The intersection is a. 4. A plane that passes through one nappe of the double-napped cone and is at an angle of 50º from the axis of the cone The intersection is an. 5. Sketch the intersection of a plane and a double-napped cone so that the intersection is a point. Chapter l Assignments 177
6. Sketch the intersection of a plane and a double-napped cone so that the intersection is a line segment. 7. Sketch the intersection of a plane and a double-napped cone so that the intersection is intersecting line segments. 8. Sketch the intersection of a plane and a double-napped cone so that the intersection is a circle. 178 Chapter l Assignments
Name Date 9. Sketch the intersection of a plane and a double-napped cone so that the intersection is a parabola. Chapter l Assignments 179
180 Chapter l Assignments
Assignment Assignment for Lesson.2 Name Date Circles Writing Equations of Circles in General and Standard Form Rewrite the equation of the circle in standard form. Then identify the center and radius of the circle. 1. y 2 36 x 2 2. 2y 2 10 2x 2 3. x2 y 2 1 4. 4x 2 4(50 y 2 ) 2 5. x 2 y 2 6x 7 0 6. x 2 y 2 2x 2y 7 7. x 2 y 2 4 4y 8. x 2 10x 74 2y y 2 Chapter l Assignments 181
Identify the center and radius of each circle. Then, write the equation of the circle in standard form. 9. y 10. y 6 5 4 3 2 1 6 5 4 3 2 1 5 4 3 2 1 0 1 2 3 4 5 6 1 2 3 4 5 x 5 4 3 2 1 0 1 2 3 4 5 6 1 2 3 4 5 x. y 12. y 2 4 2 0 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18 20 x 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 0 1 x 182 Chapter l Assignments
Assignment Assignment for Lesson.3 Name Date Your Circle is in my Line, Your Line is in my Circle Intersection of Circles and Lines 1. Use the following system of equations to complete parts (a) through (c). ( x 4) 2 ( y 3) 2 25 x 2y 5 a. Sketch the circle and the line on the following grid. b. Estimate the solution(s) to the system of equations. c. Check the solution(s) using the original equations. Chapter l Assignments 183
Solve each system of equations algebraically. Check each solution using the original equations. 2. x 2 4x y 2 8y 16 2x 2y 8 184 Chapter l Assignments
Name Date 3. x 2 y 2 29 y 2.5x 14.5 Chapter l Assignments 185
Solve each system of equations using a graphing calculator. 4. ( x 3) 2 ( y 5) 2 12 5. 3x 2 3y 2 80 y 3x 6 y 1 2 x 1 186 Chapter l Assignments
Assignment Assignment for Lesson.4 Name Date Going Off on a Tangent (Line) Tangent Lines 1. The center of a circle is ( 4, 1) and its radius is 5 units. Determine the equation of the line tangent to the circle at the point ( 7, 3). 2. The graph of a circle and its center (5, 4) are shown. Determine the equation of the line tangent to the circle at the point (10, 9). Then graph the tangent line on the grid shown. y 10 8 6 4 2 (5, 4) 6 4 2 2 4 6 8 10 x 2 4 6 Chapter l Assignments 187
3. The equation of a circle is ( x 1) 2 ( y 6) 2 40. Determine the equation of the line tangent to the circle at the point ( 3, 12). 4. The equation of a circle is x 2 4x y 2 6y 87. Determine the equation of the line tangent to the circle at the point (4, ). 188 Chapter l Assignments
Name Date 5. The center of a circle is (0, 0) and the circle is tangent to the line y 2 x 4. 3 Determine the equation of the circle. Chapter l Assignments 189
190 Chapter l Assignments
Assignment Assignment for Lesson.5 Name Date Circles, Circles, All About Circles Intersections of Two Circles Graph the system of circles on the coordinate grid. Then estimate the solution to the system of circles using the graph. 1. ( x 4) 2 ( y 3) 2 25 2. ( x 6) 2 ( y 2) 2 64 ( x 4) 2 ( y 1) 2 9 ( x 4) 2 y 2 16 Chapter Assignments 191
Solve the system of circles algebraically by using the elimination process. Include a sketch of the system of circles. 3. ( x 2) 2 ( y 8) 2 4 ( x ) 2 ( y 8) 2 49 192 Chapter l Assignments
Name Date 4. x 2 4x y 2 4y 42 x 2 2x y 2 4y 20 0 Chapter l Assignments 193
Solve the system of circles using a graphing calculator. Include a sketch of the system of circles. 5. ( x 3) 2 ( y 6) 2 36 6. 2x 2 8x 2y 2 24y 18 ( x 9) 2 ( y ) 2 9 ( x 2) 2 ( y 6) 2 49 194 Chapter l Assignments
Assignment Assignment for Lesson.6 Name Date Get Into Gear Circles and Problem Solving 1. An architect is designing a clock tower and has asked an artist to sketch the design for the circular face of the clock. a. The artist uses a coordinate plane to define the location of the face of the clock and the numbers on the clock. He places the center of the face of the clock at the origin with a radius of 12 centimeters, as shown. Write an equation for the face of the clock. 12 cm b. The artist needs to sketch the numbers on the clock. To determine where to place the numbers, he sketches a circle on the inside of the face of the clock that is 2 centimeters in from the outer edge, as shown. Write an equation for the circle that represents the location of the numbers. 10 9 12 1 2 3 2 cm 8 7 6 5 4 Chapter l Assignments 195
c. The artist sketches the numbers so that they are evenly spaced apart, as shown. What is the measure of each angle between consecutive numbers? Explain. 10 12 1 2 9 3 8 7 6 5 4 d. The equation y 3 x represents the equation of the line that extends from the number 1 to the number 7 on the face of the clock. Write an equation that represents the line that extends from the number 4 to the number 10. Explain. e. The equation y 3 x represents the equation of the line that extends from the 3 number 2 to the number 8. Write an equation that represents the line that extends from the number 5 to the number. Explain. 196 Chapter l Assignments
Name Date f. Determine the coordinates of the point that represents the number 4. g. Determine the coordinates of the point that represents the number. Chapter l Assignments 197
198 Chapter l Assignments