Exam: 8.07a Module Eight Practice Test Warning There is a checkbox at the bottom of the exam form that you MUST check prior to submitting this exam. Failure to do so may cause your work to be lost. Question 1 (Multiple Choice Worth 1 points) Find the vertex, focus, directrix, and focal width of the parabola. Vertex: (0, 0); Focus: (0, 10); Directrix: y = 10; Focal width: 160 0); Directrix: x = 10; Focal width: 160 width: 40 Vertex: (0, 0); Focus: (20, Vertex: (0, 0); Focus: (0, 10); Directrix: y = 10; Focal Vertex: (0, 0); Focus: (0, 10); Directrix: y = 10; Focal width: 10 Question 2 (Multiple Choice Worth 1 points) Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = 2. y2 = 2x y2 = 8x Question 3 (Multiple Choice Worth 1 points) Find the standard form of the equation of the parabola with a focus at (8, 0) and a directrix at x = 8. y2 = 16x Question 4 16y = x2 (Multiple Choice Worth 1 points) A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide at the base, as shown below. Find an equation for the parabola if the vertex is put at the origin of the coordinate system. y2 = 21x x2 = 21y Question 5 x2 = 5.3y y2 = 5.3x (Multiple Choice Worth 1 points) Find the center, vertices, and foci of the ellipse with equation Center: (0, 0); Vertices: (15, 0), (15, 0); Foci: (0, 9), (0, 9) (0, 15); Foci: (9, 0), (9, 0) . Center: (0, 0); Vertices: (0, 15), Center: (0, 0); Vertices: (0, 15), (0, 15); Foci: (0, 12), (0, 12) Center: (0, 0); Vertices: (15, 0), (15, 0); Foci: (12, 0), (12, 0) Question 6 (Multiple Choice Worth 1 points) Find the center, vertices, and foci of the ellipse with equation 2x 2 + 8y2 = 16. Center: (0, 0); Vertices: ; Foci: Center: (0, 0); Vertices: (8, 0), (8, 0); Foci: Center: (0, 0); Vertices: (0, 8), (0, 8); Foci: Question 7 Question 8 ; Foci: (Multiple Choice Worth 1 points) Graph the ellipse with equation Center: (0, 0); Vertices: . (Multiple Choice Worth 1 points) Find an equation in standard form for the ellipse with the vertical major axis of length 10 and minor axis of length 8. Question 9 (Multiple Choice Worth 1 points) Find the vertices and foci of the hyperbola with equation Vertices: (1, 3), (1, 13); Foci: (1, 13), (1, 3) 1) Vertices: (1, 1), (1, 11); Foci: (1, 15), (1, 5) . Vertices: (3, 1), (13, 1); Foci: (13, 1), (3, Vertices: (1, 1), (11, 1); Foci: (15, 1), (5, 1) Question 10 (Multiple Choice Worth 1 points) Graph the hyperbola with equation Question 11 . (Multiple Choice Worth 1 points) Find an equation in standard form for the hyperbola with vertices at (0, 2) and foci at (0, 11). Question 12 (Multiple Choice Worth 1 points) Find an equation in standard form for the hyperbola with vertices at (0, 8) and asymptotes at Question 13 (Multiple Choice Worth 1 points) Eliminate the parameter. x = t 3, . Question 14 (Multiple Choice Worth 1 points) Find the rectangular coordinates of the point with the polar coordinates Question 15 (Multiple Choice Worth 1 points) Find all polar coordinates of point P where P = (1, (1, + 2n) or (1, + n) or (1, Question 16 . + (2n + 1)) + n) (1, . (1, + (2n + 1)) or (1, + 2n) or (1, + 2n) + 2n) (Multiple Choice Worth 1 points) Determine two pairs of polar coordinates for the point (3, 3) with 0 < 360. (3 3 , 315), (3 , 225) (3 Question 17 , 135) , 135), (3 (3 , 225), (3 , 45) (3 , 45), ( , 315) (Multiple Choice Worth 1 points) The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. [5, 5] by [5, 5] r = 2 + 3 cos Question 18 r = 3 + 2 cos r = 2 + 2 cos (Multiple Choice Worth 1 points) r = 4 + cos Determine if the graph is symmetric about the xaxis, the yaxis, or the origin. r = 4 4 cos No symmetry Question 19 xaxis only yaxis only Origin only (Essay Worth 1 points) A railroad tunnel is shaped like a semiellipse, as shown below. The height of the tunnel at the center is 58 ft, and the vertical clearance must be 29 ft at a point 21 ft from the center. Find an equation for the ellipse. Question 20 (Essay Worth 1 points) Determine if the graph is symmetric about the xaxis, the yaxis, or the origin. r = 4 cos 5