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Lesson Worksheet: Equation of a Straight Line: Parametric Form Mathematics

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In this worksheet, we will practice finding the equation of a straight line in parametric form using a point on the line and the vector direction of the line.

Q1:

The vector equation of a straight line is given by r=⟨−1,3⟩+𝑘⟨5,2⟩. Which of the following pairs of parametric equations represents this straight line?

  • A𝑥=2+5𝑘, 𝑦=3−𝑘
  • B𝑥=5−𝑘, 𝑦=2+3𝑘
  • C𝑥=−1+5𝑘, 𝑦=3+2𝑘
  • D𝑥=2+3𝑘, 𝑦=5−𝑘
  • E𝑥=3+2𝑘, 𝑦=−1+5𝑘

Q2:

Find the parametric equations of the straight line that passes through the point (−9,8) with direction vector ⟨4,−7⟩.

  • A𝑥=8−7𝐾, 𝑦=−9+4𝐾
  • B𝑥=−9+8𝐾, 𝑦=4−7𝐾
  • C𝑥=8+4𝐾, 𝑦=−9−7𝐾
  • D𝑥=−9+4𝐾, 𝑦=8−7𝐾

Q3:

Fill in the blank: The direction vector of the straight line whose parametric equations are 𝑋=5𝑘+2 and 𝑌=−3 is .

  • A⟨0,−3⟩
  • B⟨0,5⟩
  • C⟨5,0⟩
  • D⟨−3,5⟩
  • E⟨5,−3⟩

Q4:

Fill in the blank: If straight line 𝐿 passes through the point 𝑁(3,4) and has a direction vector u=⟨2,−5⟩, then the parametric equations of line 𝐿 are .

  • A𝑥=3+2𝑘, 𝑦=4−5𝑘
  • B𝑥=−2−3𝑘, 𝑦=5+4𝑘
  • C𝑥=−3−2𝑘, 𝑦=−4+5𝑘
  • D𝑥=2+3𝑘, 𝑦=−5+4𝑘

Q5:

Fill in the blank: The direction vector of the straight line whose parametric equations are 𝑋=2 and 𝑌=−2𝑘+4is .

  • A⟨2,−2⟩
  • B⟨2,4⟩
  • C⟨0,4⟩
  • D⟨0,−2⟩

Q6:

A straight line passes through point (1,6) and has a slope of 12. Which of the following pairs of parametric equations represents this straight line?

  • A𝑥=1+4𝑘, 𝑦=6+𝑘
  • B𝑥=2+𝑘, 𝑦=1+6𝑘
  • C𝑥=1+𝑘, 𝑦=6+2𝑘
  • D𝑥=1+6𝑘, 𝑦=2+𝑘
  • E𝑥=1+4𝑘, 𝑦=6+2𝑘

Q7:

Which of the following are the parametric equations of the line through point 𝐴(−8,8) with a direction perpendicular to vector u=⟨−6,7⟩?

  • A𝑥=−8+7𝐾, 𝑦=8−6𝐾
  • B𝑥=−8+8𝐾, 𝑦=−6+7𝐾
  • C𝑥=−8+7𝐾, 𝑦=8+6𝐾
  • D𝑥=−8−6𝐾, 𝑦=8+7𝐾

Q8:

Find the parametric equation of the line that passes through the midpoint of 𝐴𝐵, where 𝐴=(2,−1) and 𝐵=(4,3), and point (2,−3).

  • A𝑥=1−4𝑘, 𝑦=3−𝑘
  • B𝑥=3−𝑘, 𝑦=1+4𝑘
  • C𝑥=3−𝑘, 𝑦=1−4𝑘
  • D𝑥=−3−𝑘, 𝑦=−1−4𝑘
  • E𝑥=3+𝑘, 𝑦=1−4𝑘

Q9:

If 𝐴𝐵 is the diameter of a circle with center 𝑀, where 𝐴=(3,2) and 𝐵=(1,2), then which of the following are parametric equations for the line that passes through 𝑀 and point (4,1)?

  • A𝑥=2−𝑘, 𝑦=2+2𝑘
  • B𝑥=2+2𝑘, 𝑦=2−𝑘
  • C𝑥=2−2𝑘, 𝑦=2−𝑘
  • D𝑥=2+2𝑘, 𝑦=2+𝑘
  • E𝑥=2+2𝑘, 𝑦=2

Q10:

Find the parametric equations of the straight line that makes an angle of 135∘ with the positive 𝑥-axis and passes through the point (1,−15).

  • A𝑥=1+𝐾, 𝑦=1−15𝐾
  • B𝑥=−15−𝐾, 𝑦=1+𝐾
  • C𝑥=1, 𝑦=−15−𝐾
  • D𝑥=1+𝐾, 𝑦=−15−𝐾

This lesson includes 37 additional questions and 171 additional question variations for subscribers.

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