Worksheet: The Equation of a Tangent to a Circle

In this worksheet, we will practice finding the equation of a tangent to a circle using the coordinates of the circle’s center and a point of tangency.

Q1:

Suppose that 𝐴𝐵 is a diameter of a circle center (7,4). If 𝐵(8,6), what is the general equation of the tangent to the circle at 𝐴?

  • A𝑥+2𝑦10=0
  • B2𝑥𝑦10=0
  • C𝑥+2𝑦+10=0
  • D𝑥2𝑦+10=0

Q2:

A circle with center 𝑀 has a diameter 𝐶𝐷, where 𝐷 is on the circumference. Given that the coordinates of the points 𝑀 and 𝐷 are 112,1 and (7,7), respectively, determine the equation of the tangent to the circle at the point 𝐶.

  • A𝑦=163𝑥394
  • B𝑦=163𝑥334
  • C𝑦=316𝑥394
  • D𝑦=316𝑥334

Q3:

Suppose that 𝐴𝐵 is a diameter of a circle center (5,4). If 𝐵(6,0), what is the general equation of the tangent to the circle at 𝐴?

  • A𝑥4𝑦28=0
  • B4𝑥+𝑦+28=0
  • C𝑥4𝑦+28=0
  • D𝑥+4𝑦+28=0

Q4:

The equation of the given graph is 𝑥+𝑦=100. Find the equation of the tangent at the point (6,8).

  • A𝑦=18𝑥354
  • B𝑦=43𝑥16
  • C𝑦=34𝑥72
  • D𝑦=34𝑥252
  • E𝑦=16𝑥9

Q5:

For the equation 𝑥+𝑦=25 find the equation of the tangent at the point (3,4).

  • A𝑦=13𝑥+3
  • B𝑦=34𝑥+74
  • C𝑦=43𝑥
  • D𝑦=14𝑥+134
  • E𝑦=34𝑥+254

Which of the following is the graph of the circle along with the tangent line found in the first part?

  • A
  • B
  • C
  • D
  • E

Q6:

A circle has the equation 𝑥+𝑦=25. Find the gradient of the tangent at the point (4,3).

  • A43
  • B34
  • C14
  • D34
  • E13

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