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Exam 10: Conics, Parametric Equations, and Polar Coordinates

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Exam 1: Preparation for Calculus125 Questionsadd course
Exam 2: Limits and Their Properties85 Questionsadd course
Exam 3: Differentiation193 Questionsadd course
Exam 4: Applications of Differentiation154 Questionsadd course
Exam 5: Integration184 Questionsadd course
Exam 6: Differential Equations93 Questionsadd course
Exam 7: Applications of Integration119 Questionsadd course
Exam 8: Integration Techniques and Improper Integrals130 Questionsadd course
Exam 9: Infinite Series181 Questionsadd course
Exam 10: Conics, Parametric Equations, and Polar Coordinates114 Questionsadd course
Exam 11: Vectors and the Geometry of Space130 Questionsadd course
Exam 12: Vector-Valued Functions85 Questionsadd course
Exam 13: Functions of Several Variables173 Questionsadd course
Exam 14: Multiple Integration143 Questionsadd course
Exam 15: Vector Anal142 Questionsadd course
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The parametric equations for the path of a projectile launched at a height h feet above the ground, at an angle The parametric equations for the path of a projectile launched at a height h feet above the ground, at an angle with the horizontal and having an initial velocity of feet per second is given by and . The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit 2 feet above the ground. It leaves the bat at an angle of degrees with the horizontal at a speed of 110 miles per hour as shown in the figure. Write a set of parametric equations for the path of the ball. ​ ​ with the horizontal and having an initial velocity of The parametric equations for the path of a projectile launched at a height h feet above the ground, at an angle with the horizontal and having an initial velocity of feet per second is given by and . The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit 2 feet above the ground. It leaves the bat at an angle of degrees with the horizontal at a speed of 110 miles per hour as shown in the figure. Write a set of parametric equations for the path of the ball. ​ ​ feet per second is given by The parametric equations for the path of a projectile launched at a height h feet above the ground, at an angle with the horizontal and having an initial velocity of feet per second is given by and . The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit 2 feet above the ground. It leaves the bat at an angle of degrees with the horizontal at a speed of 110 miles per hour as shown in the figure. Write a set of parametric equations for the path of the ball. ​ ​ and The parametric equations for the path of a projectile launched at a height h feet above the ground, at an angle with the horizontal and having an initial velocity of feet per second is given by and . The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit 2 feet above the ground. It leaves the bat at an angle of degrees with the horizontal at a speed of 110 miles per hour as shown in the figure. Write a set of parametric equations for the path of the ball. ​ ​ . The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit 2 feet above the ground. It leaves the bat at an angle of The parametric equations for the path of a projectile launched at a height h feet above the ground, at an angle with the horizontal and having an initial velocity of feet per second is given by and . The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit 2 feet above the ground. It leaves the bat at an angle of degrees with the horizontal at a speed of 110 miles per hour as shown in the figure. Write a set of parametric equations for the path of the ball. ​ ​ degrees with the horizontal at a speed of 110 miles per hour as shown in the figure. Write a set of parametric equations for the path of the ball. ​ The parametric equations for the path of a projectile launched at a height h feet above the ground, at an angle with the horizontal and having an initial velocity of feet per second is given by and . The center field fence in a ballpark is 10 feet high and 400 feet from home plate. The ball is hit 2 feet above the ground. It leaves the bat at an angle of degrees with the horizontal at a speed of 110 miles per hour as shown in the figure. Write a set of parametric equations for the path of the ball. ​ ​ ​

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Question 101

Find a polar equation for the ellipse with its focus at the pole and vertices Find a polar equation for the ellipse with its focus at the pole and vertices . .

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Question 102

The path of a projectile is modeled by the parametric equations The path of a projectile is modeled by the parametric equations and where x and y are measured in feet. Use the integration capabilities of a graphing utility to approximate the arc length of the path. Round your answer to one decimal place. ​ and The path of a projectile is modeled by the parametric equations and where x and y are measured in feet. Use the integration capabilities of a graphing utility to approximate the arc length of the path. Round your answer to one decimal place. ​ where x and y are measured in feet. Use the integration capabilities of a graphing utility to approximate the arc length of the path. Round your answer to one decimal place. ​

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Question 103

Find the arc length of the curve on the given interval. ​ Find the arc length of the curve on the given interval. ​

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Question 104

Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results. Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results.

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Question 105

Find the vertex, focus, and directrix of the parabola and sketch its graph. Find the vertex, focus, and directrix of the parabola and sketch its graph.

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Question 106

Find a polar equation for the hyperbola with its focus at the pole, eccentricity Find a polar equation for the hyperbola with its focus at the pole, eccentricity , and directrix . , and directrix Find a polar equation for the hyperbola with its focus at the pole, eccentricity , and directrix . .

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Question 107

For the given point in polar coordinates, find the corresponding rectangular coordinates for the point. For the given point in polar coordinates, find the corresponding rectangular coordinates for the point. . ​ . ​

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Question 108

Find an equation of the ellipse with vertices Find an equation of the ellipse with vertices and eccentricity . ​ and eccentricity Find an equation of the ellipse with vertices and eccentricity . ​ . ​

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Question 109

Find a polar equation for the ellipse with its focus at the pole, eccentricity Find a polar equation for the ellipse with its focus at the pole, eccentricity , and directrix . , and directrix Find a polar equation for the ellipse with its focus at the pole, eccentricity , and directrix . .

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Question 110

Find the length of the curve Find the length of the curve over the interval . Round your answer to two decimal places. ​ over the interval Find the length of the curve over the interval . Round your answer to two decimal places. ​ . Round your answer to two decimal places. ​

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Question 111

Find Find . . Find .

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Question 112

Write the corresponding rectangular equation for the curve represented by the parametric equations Write the corresponding rectangular equation for the curve represented by the parametric equations by eliminating the parameter. by eliminating the parameter.

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Question 113

Find the second derivative Find the second derivative of the parametric equations . ​ of the parametric equations Find the second derivative of the parametric equations . ​ . ​

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Question 114
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