7. r = r = r = r = r = 2 5

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1 Exercise a: I. Write the equation in standard form of each circle with its center at the origin and the given radius.. r = 4. r = 6 3. r = 7 r = 5 5. r = 6. r = 6 7. r = r =.5 9. r = 4 0. r = 3. r = 3. r = 5 II. Find the center and radius for each circle with the given equation and graph each circle. 3. x + y = 6 x + y = x + y = x + y = x + y 44 = 0 8. x 49 + y = 0 9. x = 64 y 0. y = x. x + y = 6. 5x = 5 5y 3. 3x + 3y = 48 6x = 6y Exercise b: I. Find the center and radius of the circle with the given equation. Graph the circle.. (x 7) + (y 5) =. (x ) + (y ) = 8 3. (x + 3) + (y + ) = 49 (x + 6) + (y + 8) = 9 5. (x + 5) + (y 4) = 6. (x 3) + (y + 3) = 0 7. x + (y 3) = (x ) + y = (x + ) + y = 4 0. x + (y + 3) = 8 II. Write an equation in standard form of the circle with the given center and radius.. (, ); 5. ( 5, 6); 4 3. (, 0); (0, 3); 9 5. ( 3, 5); 4 6. (, ); (4, 3 ); 8. ( 0, ); 7 9. (, 3 ); 5 0. (5, 3); 4

2 Exercise c: Rewrite each equation in standard form. Find the center and radius.. x + y 4x 6y 3 = 0. x + y + x + 6y + 84 = 0 3. x + y + y = 5 x + y 4x = 8 5. x + 8x + y y = x 0x + 5y 50y = x + 4y + 36y = 5 8. x x + y = 9. 3(x + y + 4) = 6y x 0. 3x x 4 = y + y Exercise a: I. Find the center, foci, lengths of the major a nd minor axes, and sketch the graph of each of the following ellipses II. Write each of the following in standard form of an ellipse, tell whether the ellipse if horizontal or vertical, find the coordinates of the foci and the lengths of the major and minor axes. 7. 4x + 5y = x + y = y = 64 4x 0. 9x 00 = 44 4y. 5x + 0y = 00. x + y = Exercise b: I. Find the center, the coordinates of the vertices and sketch the graph.. ( x ) ( y ) 4 9. ( x 5) ( y ) x ( y ) 49 9 ( x 3) y ( x 6) ( y ) 8 6 II. Find the equation of the ellipse with the information given. 6. ( x 7) ( y 5) 0 7. Center at (, 5) 8. Center at ( 4, ) major axis vertical. foci at ( 7, ) and (, ) a = 5, b = 4. length of major axis 9. Center at (3, ) 0. Vertical ellipse major axis horizontal. vertices of the major axis are length of major axis: 0. at (, 5) & (, 0) length of minor axis: 4. length of minor axis: 4

3 Exercise c: I. Write each in standard form of an ellipse then sketch their graphs.. 9x + 4y 4y = 0. x + x + y = 3. 4x 40x + y + 6y = 05 6x + 64x + 5y 50y = II. Find the center and foci of each of the following ellipses. 5. x x + 3y 6y = x + 30x + 4y + 8y = x + 4y x 8y = x + 3y + 4x + 4y = 9. 5x 00x + y + y = 0. x 0x + 4y + 4y = 3 Exercise 3a: Draw the graphs of the following Exercise 3b: x y 9. 6 ( x ) ( y ) 9 6 * *use the same rule for center as an ellipse. I. Find the vertices, foci, and equations of the asymptotes for each of the following hyperbola. Draw the graph II. Write the following hyperbola in standard form, then find their vertices, foci, and equations of the asymptotes. 5. 5y x = x y = y 9x = x 6y = y 5x = x 9y = 45. 4x = + 3y. 4y 4y x + 0x = 5* *use the same rule as an ellipse.

4 Exercise 3c: Write the equation in standard form, for each hyperbola described below.. Vertices: (±, 0). Vertices: (0, ±4) Asymptotes: y = ± 3 x. Asymptotes: y = ± 5 4 x 3. Foci: (0, ±3 5 ) Foci: (±5, 0) Asymptotes: y = ±x. Asymptotes: y = ± 4 3 x 5. Vertices: (±3, 0) 6. Vertices: (0, ±9) Foci: (± 34, 0). Foci: (0, ± 06 ) 7. Vertices: (0, ±) 8. Vertices: (±, 0) Foci: (0, ± 5 ). Foci: (± 9, 0) Exercise 4a: For each parabola, sketch the graph, include the vertex and axis of symmetry.. y = 3 x. y = 3x 3. x = y x = y 5. y = x 6. 4y = x 7. y + 3x = 0 8. x y = 0 Exercise 4b: I. For each parabola, sketch the graph include the vertex and axis of symmetry.. y = (x ) + 3. y = 4(x + ) + 3. x = 3 (y 3) 5 x = (y + 4) II. State the vertex, axis of symmetry, and direction of opening. 5. y = x y = 3(x + ) 6 7. x = (y ) x = (y + ) + 9. x = y 5 0. y = 3 (x 4) + 3 Exercise 4c: I. Rewrite each equation in Standard Form of a Parab ola, then sketch the graph.. 6y = x. y = 8 x 3. (y ) = 3x 4(x + 3) = y 5. (y + ) + (x + 5) = 0 6. y = x 6x + 5

5 II. Rewrite each equation in Standard Form of a Parabola, then state the vertex, axis of symmetry, and direction of opening. 7. x = y + 8y y = x 0x y = x + 6x + 0. x = y + y. y = x x. y = 3x + 6x y = 3x 4x 50 x = y + 8y + 5. x = 3y + y + 5 Exercise 4d: I. Sketch the graph for each parabola, include the vertex, focus and directrix [clearly label the coordinates or equations for each].. y = 4 x. x = 3 4 y + 3. x = (y + ) y = 8 (x ) + II. Find the coordinates of the vertex, focus and the equation of the directrix. 5. y = 0 x 6. y = (x ) x = 6 y + 8. x = 8(y ) y = 3(x + 4) 7 0. y = 3 (x ) 3 Exercise 4e: I. Write the equation in standard form of a parabola.. F:(0, 3); Directrix: y = 3. F:(7, 0); Directrix: x = 3. F:( 4, ); Directrix: x = 0 F:( 4, ); Directrix: y = 0 5. F:(0, 0); Directrix: y = 6. F:(0, ); Directrix: x = 4 II. For each parabola, sketch the graph and label the vertex, then write the equation. 7. F:(0, ); Directrix: y = 8. F:(, ); Directrix: y = 0 9. F:(, 0); Directrix: x = 0. F:(, ); Directrix: x = 0 Exercise 5a: Identify the following equation as a Circle, Ellipse, Hyperbola, or Parabola.. x + y = 6. y = (x 5) x = (y + 7) ( y 4) ( x ) x = 9 y 8. x 4y = 6 9. x + y 4x + 6y + = 0 0. x + y = 0. 4x = y x (x + 4) + 9(y 3) = y = x x 4y + y = 5. 3x + 3y 6x = 8

6 Exercise 5b:. Find the equation of a circle that passes through the origin and has its center at (5, ).. A circle has a diameter with endpoints ( 7, 5) and (, ). Find the equation of the circle. 3. P(, ), Q(4, 3), and R(5, 0) are vertices of a triangle that is inscribed in a circle. Find the equation of the circle. A pool table is shaped as an ellipse, with its major axis 8 feet long and its minor axis feet long. If a cue ball places at one foc us is struck so that it bounces off one cushion and stops at the other focus point, how far has the cue ball traveled? 5. The grass area in front of the local city hall is in the shape of an ellipse, 40 feet wide and 00 feet long. There is a flag pole a t each focus. How far apart are the flag poles? 6. The ellipse with equation 5x + 6y 400 = 0 is moved 5 units to the right and 3 units down. Find the equation of the ellipse in its new position. 7. Graph ( x ) ( y ) 6 9. Hint: use the basic graph for x y Write the equation y 4x 6y + 3x 7 = 0 in standard form for a hyperbola which does not have its center at its origin. 9. Draw the graph of xy = 6, then give the equation of the asymptotes [Hint: solve for y, then make a table of values to plot points]. 0. Find the equation of the parabola which has points at (0, 7) & (, 5) and the axis of symmetry is x =.. In a suspension bridge the horizontal distance between the supports is the span of the bridge, and the vertical distance between the points where the cable is attached to the supports and the lowest point of the cable is the sag. The span of the George Washington Bridge is 3500 feet, and its sag is 36 feet. Find an equation of the parabola that represents the cable.. The center of gravity of a long jumper during a given jump traces a curve given by y = 54 x + 3 x + 3 where y is the height of center of gravity at each point of x [the length of the jump]. Determine the maximum height of the center of gravity during the jump. Hint: complete the square to put into standard form, don t forget to distribute the negative.