Question

what is the equation of the circle with a center at (-5, -4) and a diameter of 10 units? enter an answer in each box to complete the equation. be sure to include a plus or minus symbol where needed. (x )^2+(y )^2=

Explanation:

Step1: Recall the standard circle - equation

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 the center coordinates

Given the center of the circle is $(-5,-4)$, so $h=-5$ and $k = - 4$.

Step3: Calculate the radius

The diameter $d = 10$ units. Since $r=\frac{d}{2}$, then $r=\frac{10}{2}=5$ units.

Step4: Substitute values into the equation

Substitute $h=-5$, $k = - 4$, and $r = 5$ into the standard - form equation:
$(x-(-5))^2+(y-(-4))^2=5^2$, which simplifies to $(x + 5)^2+(y + 4)^2=25$.

Answer:

$(x + 5)^2+(y + 4)^2=25$