Name: Class: Date: Conics Multiple Choice Pre-Test. Multiple Choice Identify the choice that best completes the statement or answers the question.
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1 Name: Class: Date: Conics Multiple Choice Pre-Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1 Graph the equation x 2 + y 2 = 36. Then describe the graph and its lines of symmetry. C The graph is a circle of radius 6. Its center is at the origin. Every line through the center is a line of symmetry. D The graph is a circle of radius 36. Its center is at the origin. Every line through the center is a line of symmetry. The graph is a circle of radius 6. Its center is at the origin. The y-axis and the x-axis are lines of symmetry. The graph is a circle of radius 36. Its center is at the origin. The y-axis and the x-axis are lines of symmetry.
2 2 Graph the equation 16x 2 + 4y 2 = 49. Then describe the graph and its lines of symmetry. C The graph is an ellipse. The center is at the origin. It has two lines of symmetry, the x-axis and the y-axis. D The graph is a circle. The center is at the origin. Every line through the origin is a line of symmetry. The graph is an ellipse. The center is at the origin. It has two lines of symmetry, the x-axis and the y-axis. The graph is a circle. The center is at the origin. Every line through the origin is a line of symmetry. lgebra II Conics Pre-Test Page 2
3 3 Graph the equation x 2 y 2 = 16. Then describe the graph and its lines of symmetry. C The graph is a hyperbola. Its center is at the origin. It has four lines of symmetry, the x-axis, the y-axis, y = x, and y = x. D The graph is a hyperbola. Its center is at the origin. It has four lines of symmetry, the x-axis, the y-axis, y = x, and y = x. The graph is a circle with radius 4. Its center is at the origin. Every line through the center is a line of symmetry. The graph is a hyperbola. Its center is at the origin. It has two lines of symmetry, the x-axis and the y-axis. lgebra II Conics Pre-Test Page 3
4 4 Graph 3x y 2 = 84. C D 5 Write an equation of a parabola with a vertex at the origin and a focus at (-2, 0). x = 1 8 y 2 C y = 1 8 x 2 y = 1 4 x 2 D x = 1 8 y 2 6 Write an equation of a parabola with a vertex at the origin and a directrix at y = 5. x = 5y 2 C y = 1 20 x 2 x = 1 20 y 2 D y = 20x 2 lgebra II Conics Pre-Test Page 4
5 7 Identify the vertex, focus, and directrix of the graph of y = 1 8 (x 2) vertex (2, 5), focus (2, 7), directrix at y = 3 C vertex (2, -5), focus (0, -9), directrix at y = -1 vertex (2, -5), focus (0, -1), directrix at y = -9 D vertex (2, 5), focus (2, 3), directrix at y = 7 8 Graph x = 1 5 y 2. C D lgebra II Conics Pre-Test Page 5
6 9 Identify the conic section. Parabola C Circle Hyperbola D Ellipse 10 When a plane intersects a cone at an angle that is parallel to the edge of the cone, what shape is formed? Parabola C Circle Hyperbola D Ellipse lgebra II Conics Pre-Test Page 6
7 11 Write an equation of an ellipse with center (3, -3), vertical major axis of length 12, and minor axis of length 6. Graph the ellipse. ( x + 3) 2 6 (y 3)2 12 = 1 C ( x + 3) 2 36 (y 3)2 9 = 1 ( x 3) (y + 3)2 6 = 1 D ( x 3) (y + 3)2 36 = 1 12 Write an equation of a circle with center (-5, 8) and radius 2. ( x + 5) + Ê Á y 8ˆ = 2 C ( x 5) + Ê Á y + 8ˆ ( x 5) + Ê Á y + 8ˆ = 2 D ( x + 5) + Ê Á y 8ˆ = 4 = 4 lgebra II Conics Pre-Test Page 7
8 13 Write an equation in standard form for the circle. ( x 1) 2 + Ê Á y 3ˆ 2 ( x + 1) 2 + Ê Á y + 3ˆ 2 = 4 C ( x + 1) + Ê Á y 3ˆ = 4 D ( x 1) + Ê Á y + 3ˆ = 4 = 4 14 Find the center and radius of the circle with equation ( x 5) + Ê Á y + 6ˆ (5, -6); 5 2 C (5, -6); 25 (-5, 6); 25 D (-5, 6); 5 = 50. lgebra II Conics Pre-Test Page 8
9 15 Graph ( x + 4) 2 + Ê Á y 7ˆ 2 = 49. C D lgebra II Conics Pre-Test Page 9
10 16 Identify the center of the hyperbola with the equation ( x 2) 2 9 center: (2, -4) C center: (-2, 4) (y + 4)2 64 = 1. Graph the hyperbola. center: (2, -4) D center: (-2, 4) lgebra II Conics Pre-Test Page 10
11 17 Graph the ellipse with the equation (x 3)2 49 (y + 2) C = 1. D In the next three questions, identify the conic section. If it is a parabola, give the vertex. If it is a circle, give the center and radius. If it is an ellipse or a hyperbola, give the center and foci. 18 4x 2 + 7y x 56y = 0 ellipse with center (4, -4) foci at (4 ± 3, -4) hyperbola with center (-4, 4) foci at (4, -4 ± 3) C ellipse with center (-4, 4) foci at ( 4 ± 3, 4) D hyperbola with center (4, -4) foci at ( 4, 4 ± 3) lgebra II Conics Pre-Test Page 11
12 19 y 2 4x + 6y + 29 = 0 parabola; vertex (-5, 3) C parabola; vertex (5, 4) parabola; vertex (5, -3) D parabola; vertex (4, 3) 20 11x 2 3y 2 88x + 18y = 0 ellipse with center (4, 3) foci at (4, -3 ± 14) hyperbola with center (4, 3) foci at (4 ± 14, 3) C ellipse with center (4, -3) foci at ( 4, 3 ± 14) D hyperbola with center (4, -3) foci at ( 3 ± 14, -4) 21 x 2 + y 2 + 8x 4y = 11 cirlce; center (-4, 2); radius = 9 C cirlce; center (-4, 2); radius = 3 cirlce; center (4,- 2); radius = 9 D cirlce; center (4,- 2); radius = 3 lgebra II Conics Pre-Test Page 12
13 22 In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measured 50 centimeters tall and 90 centimeters wide. Where should the filament be placed in the searchlight to acheive the brightest beam? cm from the vertex C cm from the vertex 5 cm from the vertex D at the vertex 23 Write an equation of a circle with center (3, -7) that goes through the point (1, 1). (x + 3) 2 + (y 7) 2 =52 C (x 3) 2 + (y + 7) 2 =32 (x 3) 2 + (y + 7) 2 =68 D (x + 3) 2 + (y 7) 2 =40 lgebra II Conics Pre-Test Page 13
14 24 Write an equation of a hyperbola with center (-4, 6) and vertices at (-8, 6) and (0, 6). Graph the hyperbola. ( x + 4) 2 16 (y 6)2 9 = 1 C (y 6)2 16 (x + 4)2 9 = 1 (y + 6)2 16 (x 4)2 9 = 1 D ( x 4) 2 16 (y + 6)2 9 = 1 25 Write an equation for the translation of x 2 + y 2 = 25, 2 units right and 4 units down. ( x + 2) 2 + Ê Á y + 4ˆ 2 ( x 2) 2 + Ê Á y + 4ˆ 2 = 25 C ( x + 2) + Ê Á y 4ˆ = 25 = 25 D ( x 2) + Ê Á y 4ˆ = 25 lgebra II Conics Pre-Test Page 14
15 26 Find the center of the ellipse with the equation ( x 3) (y 2)2 64 Center: (-3, -2) C Center: (3, 2) = 1. Graph the ellipse. Center: (-3, -2) D Center: (3, 2) lgebra II Conics Pre-Test Page 15
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