Video: Finding the Equation of a Circle

Write the equation of the circle of center (0, 5) and diameter 10.

01:18

Video Transcript

Write the equation of the circle of center zero, five and diameter 10.

The general equation of a circle is given by 𝑥 minus 𝑎 all squared plus 𝑦 minus 𝑏 all squared equals 𝑟 squared, where the center of the circle has coordinates 𝑎, 𝑏. And the radius of the circle is 𝑟. In this question, as the diameter is equal to 10, the radius must be equal to five, as the radius is half of the diameter.

Substituting in the coordinates of the center — zero, five — and the radius, five, gives us 𝑥 minus zero all squared plus 𝑦 minus five all squared equals five squared. As 𝑥 minus zero is equal to 𝑥, the left-hand side can be rewritten as 𝑥 squared plus 𝑦 minus five squared. On the right-hand side, five squared is equal to 25.

Therefore, the equation of the circle with center zero, five and diameter 10 is 𝑥 squared plus 𝑦 minus five all squared equals 25.

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