Video: Identifying the Equation of a Circle given Its Radius and Its Center Point’s Coordinates

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

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Video Transcript

Write the equation of the circle of center eight, four and radius nine.

The equation of any circle can be written 𝑥 minus 𝑎 all squared plus 𝑦 minus 𝑏 all squared is equal to 𝑟 squared, where the center of the circle has coordinates or ordered pair 𝑎, 𝑏 and the radius of the circle is equal to 𝑟.

Substituting in the coordinate eight, four into the equation gives us 𝑥 minus eight all squared plus 𝑦 minus four all squared. As the radius of the circle is equal to nine, this will be equal to nine squared.

Squaring nine gives us 81. This means that the equation of the circle is 𝑥 minus eight all squared plus 𝑦 minus four all squared equals 81. This is the equation of the circle with center eight, four and radius nine.

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