Home > Grade Levels > High School Geometry >

Finding the Equation of Circles

HSG-GPE.A.1
Answer Keys Here

Aligned To Common Core Standard:

Expressing Properties - HSG-GPE.A.1

How to Find the Equation of Circles - You must have studied a lot about these shapes? This time around, we are going to focus on how you can find the equations of these glorious figures. First, let's understand the basic definition of this shape. When all the points in a plane are joined together at a given distance (known as the radius), from a given point, which is known as the center. In a circle, there are two important features to consider. A line segment passing through the middle of a circle, connecting any two points on the is known as the diameter. Assume that x and y are two coordinate points on the circle having a center (h, k) with a radius r. Now, here we are using the Distance Formula to find the equation of the circle, which is: (x - h)2 + (y - k)2 = r2. (x2 - x1)2 + (y2 - y1)2. Substitute (x1, y1) = (h, k), (x2, y2) = (x, y) and d=r √(x - h)2+(y - k)2 = r. Square each side. (x - h)2 + (y - k)2 = r2. And you have the equation of a circle! Students can use these worksheets and lessons to learn how to determine the equation of a circle.

Printable Worksheets And Lessons




Homework Sheets

Given center points and a radius or diameter, tell us more about the circle.

  • Homework 1 - Find the equation of a circle whose center is at (3, - 3) and radius 6.
  • Homework 2 - The center and the midpoint of the line segment making the diameter AB.
  • Homework 3 - Write the equation of a circle whose diameter is 12 and whose center is at (-4, -3)?



Practice Worksheets

These questions are more diverse than the homework problems.

  • Practice 1 - The standard equation of a circle with center C (h, k) and radius r is: (x - h)2+ (y - k)2 = r2
  • Practice 2 - The midpoint formula is used to find the coordinates of the center C of the circle.
  • Practice 3 - The radius is half the distance between A and B.



Math Skill Quizzes

You will find the most commonly asked test questions here.

  • Quiz 1 - The coordinate of C and the radius are used in the standard equation of the circle to obtain the equation.
  • Quiz 2 - Substitute h, k and r in the standard equation to solve
  • Quiz 3 - What are the coordinates of the center of this circle? (x + 7)2 + (y + 3)2 = 9.


How Does This Skill Help You?

If we are able to determine this formula for this shape, we replicate this figure where and when ever we need it. In addition to being able to replicate this you can use it to model an actual structure. If an engineer can communicate this formula to an architect and the architect to foreman and the foreman to the carpenter, a competent and likely structure that can be reliably built anywhere and everywhere. So remember when you need to do anything with a circle being able to determine the formula will give you powerful information that can change how you view the world.