Equations of Circles Worksheets

How to Convert A Circle Equation into the Center - Radius Form? The equation of the circle is usually in the general form, which is a complicated form equation. However, if you convert the general equation of circle into a center-radius form or standard form, it will become easier to resolve. So, let us learn how we can convert the general equation of circle into a center-radius form. First of all, you would need to complete the square of the general form of the equation. To do that, you need to follow the steps given below. An example of the general equation of the circle is:
x2 + y2 - 4x - 6y + 8 = 0.
The first step is to start grouping the x-terms and y-terms together by moving them. You also need to move the constant terms on the right side of the equation.
x2 - 4x + y2 - 6y = -8
The next step is to put the needed values, which will create the perfect square for both x and y-related terms.
x2 - 4x + (☐) + y2 - 6y + (☐) = -8 +(☐) + (☐)
Find the missing value by taking half of the middle term of the trinomial and squaring it. Remember that the missing value will always be positive.
(x-2)2+ (y-3)2 = 5

  • Basic Lesson

    Guides students solving equations that involve equations of circles. Demonstrates answer checking. Convert this equation into center - radius form. State the coordinates of the center of the circle and its radius.

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  • Intermediate Lesson

    Demonstrates how to solve more difficult problems. Write the center - radius equation of a circle with a center at ( -2,5) and passes through the point (3,4). The radiuses obtained by using the distance formula.

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  • Independent Practice 1

    A really great activity for allowing students to understand the concept of the equations of circles.

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  • Independent Practice 2

    Students find the equations of circles in assorted problems. The answers can be found below.

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  • Homework Worksheet

    Students are provided with problems to achieve the concepts of the equations of circles.

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  • Skill Quiz

    This tests the students ability to evaluate math statements with the equations of circles.

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  • Answer Key

    Answers for math worksheets, quiz, homework, and lessons.

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What an Insult!

How dare of you to think that I am an analyst! Some mathematicians become so tense these days that they that they do not go to sleep during seminars.