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?

  • A 𝑥 + 2 𝑦 1 0 = 0
  • B 2 𝑥 𝑦 1 0 = 0
  • C 𝑥 + 2 𝑦 + 1 0 = 0
  • D 𝑥 2 𝑦 + 1 0 = 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.

  • A 𝑦 = 1 6 3 𝑥 3 9 4
  • B 𝑦 = 1 6 3 𝑥 3 3 4
  • C 𝑦 = 3 1 6 𝑥 3 9 4
  • D 𝑦 = 3 1 6 𝑥 3 3 4

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?

  • A 𝑥 4 𝑦 2 8 = 0
  • B 4 𝑥 + 𝑦 + 2 8 = 0
  • C 𝑥 4 𝑦 + 2 8 = 0
  • D 𝑥 + 4 𝑦 + 2 8 = 0

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