Question

which of the following is the equation of a circle with center (0,0) and radius 10?
a. $x^{2}+y^{2}=100$
b. $x^{2}+y^{2}=50$
c. $x^{2}+y^{2}=20$
d. $x^{2}+y^{2}=10$

Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle with center $(h,k)$ and radius $r$ is $(x - h)^{2}+(y - k)^{2}=r^{2}$.

Step2: Substitute center and radius values

Here, $h = 0,k = 0,r = 10$. So, $(x-0)^{2}+(y - 0)^{2}=10^{2}$.

Step3: Simplify the equation

$x^{2}+y^{2}=100$.

Answer:

A. $x^{2}+y^{2}=100$