14. Find the rectangular coordinates of the point with the polar coordinates. (5 points) 7. 3 O 713 2 O O NIN 28. Find an equation in standard form for the ellipse with the vertical major axis of length 16 and minor axis of length 4. (5 points) O = 1 64 4 O x2 + 1 2 8 O X + 1 8 2 O = 1 4 64'I. Determine two pairs of polar coordinates for the paint {5, 5} |with D\" 5 B at: 360\". {5 points} 0 (5 43 , 225\"}, {-5 43 , 45\") (5 43 , 315}, [-5 43 , 135) C) (5 43 , 135\"}, {-5 43 , 315} 0 (5 43 . 45}. {5 43 , 225) 17. 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] (5 points) Or = 3 + 2 cos 0 Or = 2 + 3 cos 0 Or = 2 + 2 cos 0 Or = 4 + cos 018. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -2 + 3 cos 0 (5 points) No symmetry y-axis only O x-axis only Origin only 19. A railroad tunnel is shaped like a semiellipse, as shown below. The height of the tunnel at the center is 35 ft, and the vertical clearance must be 21 ft at a point 8 ft from the center. Find an equation for the ellipse. (5 points) B i U Font Family20. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 2 cos 30 (5 points) B i U Font Family . AAA D =.1) The height of the tunnel at the center is 35 ft, and the vertical clearance must be 21 ft at a point 8 it from the center. Find an equation for the ellipse. (Show work please) (0, 35) 30 25 (8, 21) 20 10 -15 15 Equation of the ellipse: - x2 az t = = 1, we need to find a and b2 Length of semi major axis: a = 35 - x2 352 12 = 19. 1,225 12 = 1 212 82 When x = 8, y = 21 + 441 64 9 64 1,225 = 1- = 1 - 1,225 + 25 12 = 1- 9 64 9 9 64 25-9 64 16 25 62 25 25 12 25 b2 25 - 64(25) = 1662- 64(25) 1652 16 16 - 4(25) = b2 - 100 = 62 b= = 100 Then, the equation of the ellipse is: x- 1,225 100