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Course: ಪ್ರೌಢಶಾಲಾ ರೇಖಾಗಣಿತ > Unit 3
Lesson 11: Expanded equation of a circleCircle equation review
Review the standard and expanded forms of circle equations, and solve problems concerning them.
What is the standard equation of a circle?
This is the general standard equation for the circle centered at with radius .
Circles can also be given in expanded form, which is simply the result of expanding the binomial squares in the standard form and combining like terms.
For example, the equation of the circle centered at with radius is . This is its expanded equation:
Want to learn more about circle equations? Check out this video.
Practice set 1: Using the standard equation of circles
Want to try more problems like this? Check out this exercise and this exercise.
Practice set 2: Writing circle equations
Want to try more problems like this? Check out this exercise.
Practice set 3: Using the expanded equation of circles
To interpret the expanded equation of a circle, we should rewrite it in standard form using the method of "completing the square."
Consider, for example, the process of rewriting the expanded equation in standard form:
Now we can tell that the center of the circle is and the radius is .
Want to try more problems like this? Check out this exercise and this exercise.
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