Question

question 10 of 10
this circle is centered at the origin, and the length of its radius is 10. what is
the circles equation?
a. $x^{2}+y^{2}=10$
b. $x^{2}+y^{2}=100$
c. $x^{10}+y^{10}=100$
d. $x + y = 10$

Explanation:

Step1: Recall the standard equation of a circle

The standard equation of a circle centered at \((h,k)\) with radius \(r\) is \((x - h)^{2}+(y - k)^{2}=r^{2}\).

Step2: Identify the center and radius

Here, the center is \((0,0)\) (origin), so \(h = 0,k = 0\), and \(r = 10\).

Step3: Substitute into the standard equation

Substituting \(h = 0,k = 0,r = 10\) into \((x - h)^{2}+(y - k)^{2}=r^{2}\), we get \((x - 0)^{2}+(y - 0)^{2}=10^{2}\), which simplifies to \(x^{2}+y^{2}=100\).

Answer:

B. \(x^{2}+y^{2}=100\)