Question

lesson 4 homework (x - 2)^2+(y + 4)^2 = 9 to graph the circle, drag the center point to the desired location, and then drag the radius point until the radius is the desired number of units. provide your answer below.

Explanation:

Step1: Recall circle - equation form

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

Step2: Identify the center

For the equation $(x - 2)^2+(y + 4)^2=9$, comparing with the standard form, we have $a = 2$ and $b=-4$. So the center of the circle is $(2,-4)$.

Step3: Identify the radius

Since $r^2 = 9$, then $r = 3$ (we take the positive square - root as radius is a non - negative quantity).

Answer:

The center of the circle is $(2,-4)$ and the radius is $3$. To graph it, place the center point at $(2,-4)$ on the coordinate plane and then draw a circle with a radius of 3 units around that center.