Questions: Write the standard form of the equation of the circle with the given center and radius. Center (6,-2), r=sqrt(6) The equation of the circle in standard form is (x-6)^2+(y+2)^2=

Solution Steps

To write the standard form of the equation of a circle, we use the formula $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center of the circle and $r$ is the radius. Given the center $(6, -2)$ and radius $\sqrt{6}$, we can substitute these values into the formula.

Given the center $(6, -2)$ and radius $r = \sqrt{6}$.

The standard form of the equation of a circle is: $$(x - h)^2 + (y - k)^2 = r^2$$ Substitute $h = 6$, $k = -2$, and $r = \sqrt{6}$: $$(x - 6)^2 + (y - (-2))^2 = (\sqrt{6})^2$$

Simplify the equation: $$(x - 6)^2 + (y + 2)^2 = 6$$

Final Answer