Question

the equation of a circle is given below. identify the radius and the center. then graph the circle.
$x^2 + y^2 - 4y - 5 = 0$
radius:
center: ( , )

Explanation:

Step1: Rearrange the equation

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

Step2: Complete the square for y

$y^2 - 4y = (y - 2)^2 - 4$, so $x^2 + (y - 2)^2 - 4 = 5$

Step3: Simplify to standard form

$x^2 + (y - 2)^2 = 9$ (since $5 + 4 = 9$)

Step4: Identify center and radius

Standard form: $(x - h)^2 + (y - k)^2 = r^2$. Here, $h=0$, $k=2$, $r^2=9$ so $r=3$.

Answer:

Radius: 3
Center: (0, 2)
Graph: Plot center (0,2), draw circle with radius 3 on the grid.