Questions: The equation of a circle is given below. Identify the center and radius. Then graph the circle (x+5)^2+(y+2)^2=16 Center: Radius:

Transcript text: The equation of a circle is given below. Identify the center and radius. Then graph the circle \[ (x+5)^{2}+(y+2)^{2}=16 \] Center: $\square$ Radius: $\square$

Solution

Solution Steps

Step 1: Identify the center of the circle

The equation of the circle is given in the standard form $(x + 5)^2 + (y + 2)^2 = 16$. The standard form of a circle's equation is $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center of the circle and $r$ is the radius.

In this equation, $(x + 5)^2 + (y + 2)^2 = 16$, we can rewrite it as $(x - (-5))^2 + (y - (-2))^2 = 16$. Therefore, the center $(h, k)$ is $(-5, -2)$.

Step 2: Identify the radius of the circle

The radius $r$ is found by taking the square root of the right-hand side of the equation. Here, the right-hand side is 16, so $r = \sqrt{16} = 4$.

Step 3: Graph the circle

To graph the circle, plot the center at $(-5, -2)$ on the coordinate plane. Then, draw a circle with a radius of 4 units around this center.