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Video: Finding the Center and Radius of a Circle Using the Equation of a Circle

Rhodri Jones

The equation (𝑥 − 3)² + (𝑦 + 2)² = 100 describes a circle. Find its center and radius.

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Video Transcript

The equation 𝑥 minus three all squared plus 𝑦 plus two all squared equals 100 describes a circle. Find its center and radius.

The general equation of any circle is given by 𝑥 minus 𝑎 all squared plus 𝑦 minus 𝑏 all squared equals 𝑟 squared, where the center of the circle is given by the coordinates 𝑎, 𝑏 and the radius of the circle is 𝑟. In this case, in order to find the coordinates of the center of the circle, we need to solve the two equations: 𝑥 minus three equals zero and 𝑦 plus two is equal to zero.

Solving the first equation gives us 𝑥 is equal to three and solving the second equation gives us 𝑦 is equal to negative two. This means that the center of the circle has coordinates three, negative two.

In order to calculate the radius, we need to solve the equation 𝑟 squared is equal to 100. Square rooting both sides of this equation gives us 𝑟 equals root of 100. The square root of 100 is equal to 10. Therefore, the radius of the circle is 10.

A circle described by the equation 𝑥 minus three all squared plus 𝑦 plus two all squared equals 100 has center three negative two and radius 10.