Question

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 5 and 6. center (√2, √2), radius √2

Accepted Answer

Identify the center and radius of the circle. Here, the center is given as $$\left(\sqrt{2}, \sqrt{2}\right)$$ and the radius is $$\sqrt{2}. $$Recall the center-radius form of a circle's equation: $$\left(x - h\$$right)^2$$ + \left(y - k\$$right)^2$$ = r^2$, where (h$$, k)$$ is the center and r$ is the radius. Substitute the given center coordinates and radius into the formula: $$\left(x - \sqrt{2}\$$right)^2$$ + \left(y - \sqrt{2}\$$right)^2$$ = \left(\sqrt{2}\$$right)^2. $$Simplify the right side of the equation by squaring the radius: $$\left(\sqrt{2}\$$right)^2$$ = 2$$, so the equation becomes $$\left(x - \sqrt{2}\$$right)^2$$ + \left(y - \sqrt{2}\$$right)^2$$ = 2. $$For graphing, plot the center at $$\left(\sqrt{2}, \sqrt{2}\right) on $$the coordinate plane, then draw a circle with radius $$\sqrt{2}$$ units around this point.

In the following exercises, (a) find the center-radius form of the equation of each circle described, and (b) graph it. See Examples 5 and 6. center (√2, √2), radius √2

Key Concepts

Equation of a Circle in Center-Radius Form

Understanding Coordinates and Radicals

Graphing Circles on the Cartesian Plane