Question

write the standard form of the equation and the general form of the equation of the circle of radius r and center (h,k). graph the circle. (r = sqrt{8}), ((h,k)=(5, - 4)). the equation for the circle in standard form is (square). (simplify your answer.)

Explanation:

Step1: Recall circle standard - form formula

The standard - form of the equation of a circle with radius $r$ and center $(h,k)$ is $(x - h)^2+(y - k)^2=r^2$.

Step2: Substitute given values

Given $r = \sqrt{8}$, $h = 5$, and $k=-4$. Substitute these values into the formula: $(x - 5)^2+(y+4)^2=(\sqrt{8})^2$.

Step3: Simplify the right - hand side

Since $(\sqrt{8})^2 = 8$, the standard - form of the equation of the circle is $(x - 5)^2+(y + 4)^2=8$.

Answer:

$(x - 5)^2+(y + 4)^2=8$