How would you find the center and radius of x^2 + y^2 - 81 = 0?

Dec 21, 2015

Center : $\left(0 , 0\right)$; Radius : $9$.

Explanation:

First, you put the 81 at the right side, you're now dealing with ${x}^{2} + {y}^{2} = 81$.

You now recognize the square of the norm!

${x}^{2} + {y}^{2} = 81 \iff \sqrt{{x}^{2} + {y}^{2}} = \sqrt{81} = 9$.

It means that the distance between the origin and any point of the circle has to be equal to 9, you have to see ${x}^{2}$ as ${\left(x - 0\right)}^{2}$ and ${y}^{2}$ as ${\left(y - 0\right)}^{2}$ to see the origin appear. I hope I explained it well.