which equation represents a circle with a center at (-4, 9) and a diameter of 10 units?\n(x - 9)^2+(y + 4)^2…

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 the center coordinates

Given the center of the circle is $(-4,9)$, so $h=-4$ and $k = 9$.

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 formula

Substitute $h=-4$, $k = 9$, and $r = 5$ into the equation $(x - h)^2+(y - k)^2=r^2$. We get $(x-(-4))^2+(y - 9)^2=5^2$, which simplifies to $(x + 4)^2+(y - 9)^2=25$.

Answer:

$(x + 4)^2+(y - 9)^2=25$ (the second option)