Rewrite the equation in the left column into the format in the middle column. The answers are in the third column. 1. y 4y 4x 4 0 y k 4p x h y 2 4 x 0
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1 Pre-Calculus Section 1.1 Completing the Square Rewrite the equation in the left column into the format in the middle column. The answers are in the third column. 1. y 4y 4x 4 0 y k 4p x h y 4 x 0. 3x 3y 6x 1y 0 x h y k r x 1 y 5 x h y k x 1 y 3. 4x y 8x 4y x h y k x 1 y 4. 4x y 4y 8x x h y k x 1 y x 3y 8x 6y x 6x 4y 1 0 x h 4p y k x 3 4 y x h y k x y 1 7. x 3y 8x 6y x 4x y y 0 x h y k r x y 1 5 x h y k x 1 y 9. 9x 4y 18x 16y k x 1 y x 4x y 4 x h 4p y 11. x y 1x 8y 4 0 x h y k r x 3 y 5 y k x h y 1 x 1. y 4x 16x y b a 4 1 x h y k x 4 y x 3y 8x 6y x h y k x 1 y x y x y x 4x y x h 4p y k x y 16. x y 4x 4y 1 0 x h y k r x y 9 x h y k x 1 y x y 18x x y 8x 7 0 x h y k r x y 0 x h y k x 4 y x 3y 8x 6y x y 6x y 9 0 x h y k r x 3 y 1 1 1
2 Pre-Calculus Section 1. The Circle For problems 1-6, write the equation of the circle described in standard form. 1. C(4, 3), r =. C(-4, -9), r = 3 3. C(6, 0), r = The center is (, 3); the circle passes through (5, 6). 5. The points (8, 0) and (0, 6) are endpoints of a diameter. 6. The center is (5, -4) and the circle is tangent to the x-axis. For problems 7-9, for each circle below: a. Rewrite the equation in standard form. b. Identify the center of the circle. c. Identify the radius of the circle. 7. x y x 8y x y 1y x y 10x 18y 1 Pre-Calculus Section 1.3 The Parabola For each parabolelow: a. Write the coordinates of the vertex as an ordered pair. b. Write the coordinates of the focus as an ordered pair. c. Write the equation of the directrix. 1 4 y 3 1 x y 1 x. 3. x 4 y 7 4. x y 3 Given the information below about a parabola: a. Write the equation of the parabola in standard form. b. Sketch an appropriate graph of the parabola. 5. Focus (-1, 0); directrix: x = 1 6. Vertex (0, 0); Focus (5, 0) 7. Vertex (0, 0); directrix x = 4 8. Focus (0, ); directrix y = 0
3 Pre-Calculus Section 1.4 The Ellipse Given each equation below: a. Find the coordinates of the vertices and the foci. Round your values where appropriate to three decimal places. b. Sketch the curve, labeling the vertices and foci. 1. x y x 5y x 5y 5 Given the information about an ellipse, find the equation of the ellipse in standard form. 4. Center (0, 0), Vertex (7, 0); minor axis = 5. Center (0, 0), Vertex (0, -13), Focus (0, -5) Given each equation below: a. Identify the center, vertices, and foci. b. Sketch a graph of the ellipse, labeling the appropriate parts. x 5 y x y 5 4 Pre-Calculus Section 1.5 The Hyperbola For each hyperbolelow: a. Find the coordinates of the center and foci. b. Find the equations of the asymptotes. c. Sketch a graph of the hyperbola. 1. x y x y y x y 16x 400 x 6 y x 4y x 16y 19 0 Given the information below, find the equation of the hyperbola in standard form. 7. Center (0, 0), Vertex (6, 0), Focus (10, 0) 8. Center (0, 0), Vertex (0, -1), Focus (0, -13)
4 Pre-Calculus Unit 1 Review I. Given each equation below, A. Rewrite the equation in standard form. Show the work that leads to your answer. B. Identify the conic section. 1. 9y x 18y 6x x 16y 88y x 4y 3x y 6y 8x x 16y 7x 3y x y 6y 50 14x 4. x 8y 4x y 9x 36x 150y 36 0 II. Multiple Choice Choose the most correct answer and circle the letter of your choice. 9. Which of the following represents the conic section given by x 6 y 1 15? 10. Which of the following represents the conic section given by x y 1? x y 11. Which of the following represents the conic section given by 1? 16 4 x y 3 1. Which of the following represents the conic section given by 1? Which of the following represents the conic section given by x 1y 3? III. Given the information for a conic section below, write its equation in standard form. Circle your final answer. 14. the circle with center (5,-6) and radius the parabola with vertex (0,0) and focus (0,4). 16. the ellipse with foci at (0,3) and (0,-3) and vertices at (0,5) and (0,-5). 17. the circle with center (-4,) and radius the ellipse centered at (0, 1) with vertices at (5, 1) and (-5,1), and foci at (4, 1) and (-4,1). 19. the parabola with focus (-1, 3) and directrix x = the parabola with vertex (0,1) and focus (5,1).
5 IV. Sketch the graph of the conic section. Provide the information as indicated. 1. x 3 y 1 16 Center: Radius:. x 5 8y 3 Vertex: Focus: Directrix: Axis of Symmetry: y x Center: Vertices: Foci: Asymptote:
6 x 5 y Vertices: Center: Foci: Length of semi-major axis: Length of semi-minor axis: 5. y 3 4x 1 Vertex: Focus: Directrix: Axis of Symmetry:
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