Graphing Parametric Equations

Question 1

An animation features an airplane flying in a straight line across the screen from (0, 10) to (45, 160) in 5 seconds. Which parametric equations represent the onscreen path of the airplane?

Revolt · Accepted Answer

x(t) = 9t and y(t) = 30t + 10

Question 2

A jogger runs on a path at a speed of 0.075 miles per minute. A second jogger starts 5 minutes later from the same spot, but runs at a rate of 0.1 miles per minute. Create a pair of parametric equations to represent the paths of the joggers. How far down the path from the starting point does the second runner overtake the first runner?

Revolt · Accepted Answer

1.5 miles

Question 3

Which rectangular equation represents the parametric equations x = and y = 4t?

Revolt · Accepted Answer

y = 4x2, for x ≥ 0

Question 4

What is the rectangular form of the parametric equations x = 4 cos t and y = 5 sin t, where 0 ≤ t ≤ 2π?

Revolt · Accepted Answer

StartFraction x squared Over 16 EndFraction + StartFraction y squared Over 25 EndFraction = 1

Question 5

A soccer ball on the ground was kicked with an initial velocity of 35 ft/sec at an elevation angle of 40°. Create a set of parametric equations to model the path of the soccer ball. Approximately how far had the soccer ball traveled when it hit the ground?

Revolt · Accepted Answer

38 feet

Question 6

Consider the parametric equations x = 4cos(t) – 3 and y = 5sin(t) + 2. What is the rectangular form?

Revolt · Accepted Answer

StartFraction (x + 3) squared Over 16 EndFraction + StartFraction (y minus 2) squared Over 25 EndFraction = 1

Question 7

Which graph represents the parametric equations x = t2 + 2t and y = –t, where –4 ≤ t ≤ 1?

Revolt · Accepted Answer

On a coordinate plane, a curve starts at (3, negative 1), curves up through (0, 0) to (negative 1, 1), and curves up through (0, 2) and (3, 3).

Question 8

Which rectangular equation is formed by eliminating the parameter?y = t3x = t + 5

Revolt · Accepted Answer

y = x3 – 15x2 + 75x – 125

Question 9

An animation shows a beetle crawling in a straight line from the point (0, 10) to the point (28, 84) in 2 seconds. Write a pair of parametric equations to model the path of the beetle. Which point represents the location of the beetle 5 seconds after starting?

Revolt · Accepted Answer

(70, 195)

Question 10

A coach throws a football from a height of 4 feet with an initial velocity of 59 feet per second at an elevation angle of 45°. Which parametric equations represent the path of the football?

Revolt · Accepted Answer

x(t) = 59cos(45o)t and y(t) = –16t2 + 59sin(45o)t + 4

Graphing Parametric Equations Answers

More from this Course

TRY EDGENUITY HACKS