Question

write the standard equation of the circle with center (-4, -2) and r = √3. the standard form of the equation of the circle is . (type an equation. simplify your answer.)

Explanation:

Step1: Recall circle - equation formula

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

Step2: Identify values of $h$, $k$, and $r$

Given that the center is $(-4,-2)$, so $h=-4$ and $k = - 2$, and $r=\sqrt{3}$.

Step3: Substitute values into the formula

Substitute $h=-4$, $k=-2$, and $r = \sqrt{3}$ into the formula:
$(x-(-4))^2+(y - (-2))^2=(\sqrt{3})^2$.

Step4: Simplify the equation

$(x + 4)^2+(y + 2)^2=3$.

Answer:

$(x + 4)^2+(y + 2)^2=3$