Question

the equation of a circle is given in standard form. complete parts a through c to follow the step by step process to sketch the graph of the circle.
$x^{2}+y^{2}=49$
a) determine the center and radius of the circle.
the center of the circle is
(type an ordered pair )

Explanation:

Step1: Recall circle - standard form

The standard form of a circle equation is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center and $r$ is the radius.
The given equation is $x^{2}+y^{2}=49$, which can be written as $(x - 0)^2+(y - 0)^2 = 7^2$.

Step2: Determine the center

Comparing with the standard - form, when $h = 0$ and $k = 0$, the center of the circle is $(0,0)$.

Step3: Determine the radius

Since $r^{2}=49$, taking the square root of both sides (and considering the positive value for the radius), we have $r = 7$.

Answer:

The center of the circle is $(0,0)$ and the radius is $7$.