Lesson Worksheet: Equation of a Circle Mathematics • 11th Grade

In this worksheet, we will practice finding the equation of a circle using its center and a given point or the radius and vice versa.


Write the equation of the circle of center (8,4) and radius 9.

  • A(π‘₯βˆ’8)+(π‘¦βˆ’4)=81
  • B(π‘₯βˆ’8)+(π‘¦βˆ’4)=9
  • C(π‘₯+8)+(𝑦+4)=9
  • D(π‘₯+8)+(𝑦+4)=81


In the figure below, find the equation of the circle.

  • A(π‘₯βˆ’5)+(π‘¦βˆ’4)=25
  • B(π‘₯+5)+(𝑦+4)=25
  • C(π‘₯βˆ’5)+(π‘¦βˆ’4)=5
  • D(π‘₯+5)+(𝑦+4)=5


Give the general form of the equation of the circle of center (8,βˆ’2) and diameter 10.

  • Aπ‘₯+π‘¦βˆ’16π‘₯+4π‘¦βˆ’32=0
  • Bπ‘₯+𝑦+16π‘₯βˆ’4π‘¦βˆ’32=0
  • Cπ‘₯+π‘¦βˆ’16π‘₯+4𝑦+43=0
  • Dπ‘₯+𝑦+16π‘₯βˆ’4𝑦+43=0


A circle has center (2,2) and goes through the point (6,3). Find the equation of the circle.

  • A(π‘₯βˆ’2)+(π‘¦βˆ’2)=17
  • B(π‘₯βˆ’2)+(𝑦+2)=17
  • C(π‘₯+2)βˆ’(𝑦+2)=17
  • D(π‘₯+2)βˆ’(𝑦+2)=√17
  • E(π‘₯βˆ’2)+(π‘¦βˆ’2)=√17


Find the equation of the circle represented by the given figure.

  • A(π‘₯βˆ’4)+(𝑦+7)=16
  • B(π‘₯βˆ’4)+(𝑦+7)=81
  • C(π‘₯βˆ’7)+(π‘¦βˆ’4)=49
  • D(π‘₯+4)+(π‘¦βˆ’7)=81


Find the center and radius of the circle (π‘₯+4)+(π‘¦βˆ’2)=225.

  • ACenter: (βˆ’4,2), radius: 15
  • BCenter: (2,βˆ’4), radius: 15
  • CCenter: (βˆ’4,2), radius: 225
  • DCenter: (4,βˆ’2), radius: 225
  • ECenter: (βˆ’2,4), radius: 225


Find the center and the radius of the circle (π‘₯βˆ’2)+(𝑦+8)βˆ’100=0.

  • ACenter: (2,βˆ’8), radius: 10
  • BCenter: (βˆ’8,2), radius: 10
  • CCenter: (βˆ’2,8), radius: 10
  • DCenter: (2,βˆ’8), radius: 100
  • ECenter: (βˆ’8,2), radius: 100


By completing the square, find the center and radius of the circle π‘₯+6π‘₯+π‘¦βˆ’4𝑦+8=0.

  • ACenter: (2,βˆ’3), radius: 5
  • BCenter: (βˆ’3,2), radius: 5
  • CCenter: (3,βˆ’2), radius: 5
  • DCenter: (2,βˆ’3), radius: √5
  • ECenter: (βˆ’3,2), radius: √5


The blueprint of a city is in a Cartesian coordinate system, where each unit represents 5 meters. Given that the circle π‘₯+𝑦+2π‘₯+18𝑦+44=0 represents one of the city’s squares, determine the area of the square to nearest square meter. Consider ο€Όπœ‹=227.


Determine the general form of the equation of the circle that passes through the two points 𝐴(βˆ’7,1) and 𝐡(0,6), given that the circle’s center lies on the straight line 6π‘₯βˆ’π‘¦=βˆ’43.

  • Aπ‘₯+𝑦+12π‘₯βˆ’14𝑦+48=0
  • Bπ‘₯+𝑦+14π‘₯βˆ’2𝑦+13=0
  • Cπ‘₯+π‘¦βˆ’12π‘¦βˆ’1=0
  • Dπ‘₯+π‘¦βˆ’12π‘¦βˆ’38=0

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