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9-12 Integrated Math 2 Unit 7 Lesson 2

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K-5 Math 6-8 Math •9-12 Math

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Unit 7, Lesson 2

Equation of a Circle

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Integrated Math 2

Practice

Problem 1

Match each equation to its description.

circle centered at \((0,\text-4)\) with a radius of 3
circle centered at \((1,\text-4)\) with a radius of \(\sqrt{3}\)
circle centered at \((1,4)\) with a radius of \(\sqrt{3}\)
circle centered at \((1,0)\) with a radius of 3
circle centered at \((1,\text-4)\) with a radius of 3

\((x-1)^2+y^2=9\)
\(x^2+(y+4)^2=9\)
\((x-1)^2+(y-4)^2=3\)
\((x-1)^2+(y+4)^2=9\)
\((x-1)^2+(y+4)^2=3\)

Problem 2

Write an equation of a circle that is centered at \((\text-3,2)\) with a radius of 5.

\((x-3)^2+(y+2)^2=5\)
\((x+3)^2+(y-2)^2=5\)
\((x-3)^2+(y+2)^2=25\)
\((x+3)^2+(y-2)^2=25\)

Problem 3

Write an equation of the circle that has a diameter with endpoints \((12,3)\) and \((\text-18,3)\)

Problem 4

Write an equation of a circle that is centered at \((1,\text-4)\) with a radius of 10.

Problem 5

An equation of a circle is \( x^2 - 8x + 16 + y^2 + 10y + 25 = 81\).

What is the radius of the circle?
What is the center of the circle?

Problem 6

An equation of a circle is \( x^2 - 6x + 9 + y^2 + 12x + 36 = 100\).

What is the radius of the circle?
What is the center of the circle?

Problem 7

Match each equation to its description.

circle centered at \((0,\text-3)\) with a radius of 5
circle centered at \((1,\text-3)\) with a radius of \(\sqrt{5}\)
circle centered at \((1,3)\) with a radius of \(\sqrt{5}\)
circle centered at \((1,0)\) with a radius of 5
circle centered at \((1,\text-3)\) with a radius of 5

\((x-1)^2+y^2=25\)
\(x^2+(y+3)^2=25\)
\((x-1)^2+(y-3)^2=5\)
\((x-1)^2+(y+3)^2=25\)
\((x-1)^2+(y+3)^2=5\)

Problem 8

Write an equation of the circle that has a diameter with endpoints \((\text-5,4)\) and \((9,4)\).