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

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+𝑘5,2. Which of the following pairs of parametric equations represents this straight line?

  • A𝑥=2+5𝑘, 𝑦=3𝑘
  • B𝑥=5𝑘, 𝑦=2+3𝑘
  • C𝑥=1+5𝑘, 𝑦=3+2𝑘
  • D𝑥=2+3𝑘, 𝑦=5𝑘
  • 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=87𝐾, 𝑦=9+4𝐾
  • B𝑥=9+8𝐾, 𝑦=47𝐾
  • C𝑥=8+4𝐾, 𝑦=97𝐾
  • D𝑥=9+4𝐾, 𝑦=87𝐾

Q3:

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

  • A0,3
  • B0,5
  • C5,0
  • D3,5
  • E5,3

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=45𝑘
  • B𝑥=23𝑘, 𝑦=5+4𝑘
  • C𝑥=32𝑘, 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 .

  • A2,2
  • B2,4
  • C0,4
  • D0,2

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=86𝐾
  • B𝑥=8+8𝐾, 𝑦=6+7𝐾
  • C𝑥=8+7𝐾, 𝑦=8+6𝐾
  • D𝑥=86𝐾, 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=14𝑘, 𝑦=3𝑘
  • B𝑥=3𝑘, 𝑦=1+4𝑘
  • C𝑥=3𝑘, 𝑦=14𝑘
  • D𝑥=3𝑘, 𝑦=14𝑘
  • E𝑥=3+𝑘, 𝑦=14𝑘

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=2𝑘, 𝑦=2+2𝑘
  • B𝑥=2+2𝑘, 𝑦=2𝑘
  • C𝑥=22𝑘, 𝑦=2𝑘
  • 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=115𝐾
  • B𝑥=15𝐾, 𝑦=1+𝐾
  • C𝑥=1, 𝑦=15𝐾
  • D𝑥=1+𝐾, 𝑦=15𝐾

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

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