Worksheet: Equation of a Tangent

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

Q1:

Suppose that 𝐴 𝐡 is a diameter of a circle centre ( βˆ’ 7 , 4 ) . If 𝐡 ( βˆ’ 8 , 6 ) , what is the general equation of the tangent to the circle at 𝐴 ?

  • A 2 π‘₯ βˆ’ 𝑦 βˆ’ 1 0 = 0
  • B π‘₯ + 2 𝑦 βˆ’ 1 0 = 0
  • C π‘₯ + 2 𝑦 + 1 0 = 0
  • D π‘₯ βˆ’ 2 𝑦 + 1 0 = 0

Q2:

Given that 𝐢 𝐷 is a diameter of the circle 𝑀 , and the coordinates of the points 𝑀 and 𝐷 are ο€Ό βˆ’ 1 1 2 , βˆ’ 1  and ( βˆ’ 7 , 7 ) respectively, determine the equation of the tangent to the circle at the point 𝐢 .

  • A 𝑦 = 3 1 6 π‘₯ βˆ’ 3 9 4
  • B 𝑦 = βˆ’ 1 6 3 π‘₯ βˆ’ 3 3 4
  • C 𝑦 = βˆ’ 1 6 3 π‘₯ βˆ’ 3 9 4
  • D 𝑦 = 3 1 6 π‘₯ βˆ’ 3 3 4

Q3:

Suppose that 𝐴 𝐡 is a diameter of a circle centre ( 5 , βˆ’ 4 ) . If 𝐡 ( 6 , 0 ) , what is the general equation of the tangent to the circle at 𝐴 ?

  • A 4 π‘₯ + 𝑦 + 2 8 = 0
  • B π‘₯ βˆ’ 4 𝑦 βˆ’ 2 8 = 0
  • C π‘₯ βˆ’ 4 𝑦 + 2 8 = 0
  • D π‘₯ + 4 𝑦 + 2 8 = 0

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