
Understanding Parametric Equations of Tangent Lines

Interactive Video
•
Mathematics
•
11th Grade - University
•
Hard
Standards-aligned

Jackson Turner
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What are the direction numbers in the context of parametric equations of a line?
The coefficients of the parameter t
The coordinates of the point of tangency
The magnitude of the vector
The angle between the line and the vector
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in determining the parametric equations of a tangent line to a curve?
Finding the unit tangent vector
Calculating the magnitude of the vector
Determining the point of tangency
Identifying the direction numbers
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example where t equals two, what is the point of tangency?
(1, 5)
(4, 6)
(2, 3)
(3, 4)
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the unit tangent vector calculated?
By subtracting the components of the vector
By multiplying the vector by a scalar
By dividing the derivative of the vector by its magnitude
By adding the components of the vector
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why are parametric equations not unique?
Because they depend on the choice of parameter t
Because they are derived from different functions
Because they can be expressed with different direction numbers
Because they are based on arbitrary points
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example with t equals pi over four, what is the z component of the point of tangency?
pi/4
1
0
sqrt(2)
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the x component of the unit tangent vector when t equals pi over four?
-1/2
1/sqrt(2)
1/2
-1/sqrt(2)
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
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