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{7}; (h,k)=(4, - 2) the equation for the circle in standard form is \\(\square\\). (simplify your answer.)

Explanation:

Step1: Recall standard - form formula

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

Step2: Substitute given values

Given $h = 4$, $k=-2$, and $r = \sqrt{7}$, we substitute these into the formula: $(x - 4)^2+(y+2)^2=(\sqrt{7})^2$.

Step3: Simplify the equation

Since $(\sqrt{7})^2 = 7$, the standard - form equation of the circle is $(x - 4)^2+(y + 2)^2=7$.

Answer:

$(x - 4)^2+(y + 2)^2=7$