Deck 10: Parametric Equations and Polar Coordinates

Question 1

Find the area that the curve encloses.

Answer 1

Question 2

Set up, but do not evaluate, an integral that represents the length of the parametric curve.

Answer 2

Question 3

Answer 3

Question 4

Sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the
curve.

Question 5

Set up an integral that represents the length of the curve.Then use your calculator to find the
length correct to four decimal places.

Question 6

True or False?

Question 7

Question 8

Find an equation of the tangent to the curve at the point by first eliminating the parameter.

Question 9

Eliminate the parameter to find a Cartesian equation of the curve.

Question 10

Question 11

Question 12

Question 13

Question 14

True or False?

Question 15

Find the area of the region that lies inside both curves.

Question 16

Find an equation of the tangent to the curve at the point corresponding to the given value of the
parameter.

Question 17

Eliminate the parameter to find a Cartesian equation of the curve.

Question 18

Question 19

Find an equation of the tangent to the curve at the point corresponding to the given value of the
parameter.

Question 20

Using the arc length formula, set up, but do not evaluate, an integral equal to the total arc length of the
ellipse.

Question 21

Question 22

Question 23

Question 24

Find the exact area of the surface obtained by rotating the given curve about the x-axis.

Question 25

Question 26

Question 27

Question 28

Question 29

Find an equation of the hyperbola centered at the origin that satisfies the given condition.

Question 30

Question 31

Find the eccentricity of the conic.

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Find a polar equation for the curve represented by the given Cartesian equation.

Question 39

Question 40

Find the point(s) on the curve where the tangent is horizontal.

Question 41

Find the polar equation for the curve represented by the given Cartesian equation.

Question 42

Question 43

Sketch the polar curve with the given equation.

Question 44

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.

Question 45

Question 46

Question 47

Question 48

Find the exact area of the surface obtained by rotating the given curve about the x-axis.

Question 49

Question 50

Question 51

Question 52

Question 53

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Question 54

Find a polar equation for the curve represented by the given Cartesian equation.

Question 55

Question 56

Question 57

Question 58

Question 59

Question 60