Question

2.2
score: 5/13 answered: 5/13
question 6
write the equation of the circle with center: (-1, -1) and radius: √6.
enter your answer as an equation. example: y=3x^2+1, 2x+y=3
be sure your variables match those in the question

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 $(-1,-1)$, so $h=-1$, $k = - 1$, and the radius $r=\sqrt{6}$.

Step3: Substitute values into the formula

Substitute $h=-1$, $k=-1$, and $r = \sqrt{6}$ into the equation $(x - h)^2+(y - k)^2=r^2$. We get $(x-(-1))^2+(y - (-1))^2=(\sqrt{6})^2$.

Step4: Simplify the equation

$(x + 1)^2+(y + 1)^2=6$.

Answer:

$(x + 1)^2+(y + 1)^2=6$