Question

the equation of a circle is given below. identify the center and the radius. then graph the circle.
$2x^{2}+2y^{2}-8y - 42 = 0$
center: ( , )
radius:
(there is a coordinate grid on the right side and some input buttons in the middle)

Explanation:

Step1: Divide equation by 2

$x^2 + y^2 - 4y - 21 = 0$

Step2: Rearrange and complete square for y

$x^2 + (y^2 - 4y) = 21$
$x^2 + (y^2 -4y +4) = 21 +4$
$x^2 + (y-2)^2 = 25$

Step3: Identify center and radius

Standard form: $(x-h)^2 + (y-k)^2 = r^2$
Center $(h,k)=(0,2)$, radius $r=\sqrt{25}=5$

Answer:

Center: (0, 2)
Radius: 5
(Graph: Plot center (0,2), draw circle with radius 5 on the grid)