Question

question 3 of 10
what is the equation of a circle centered at the origin with radius 15?
a. $x^{3}+y^{3}=15$
b. $x^{3}+y^{3}=225$
c. $x^{2}+y^{2}=225$
d. $x^{2}+y^{2}=15$
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Explanation:

Step1: Recall the standard equation of a circle

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

Step2: Substitute the values for center and radius

Since the circle is centered at the origin \((0,0)\) (so \(h = 0,k = 0\)) and radius \(r = 15\), substituting into the formula gives \((x-0)^{2}+(y - 0)^{2}=15^{2}\).

Step3: Simplify the equation

Simplifying \((x-0)^{2}+(y - 0)^{2}=15^{2}\) results in \(x^{2}+y^{2}=225\) (because \(15^{2}=225\)).

Answer:

C. \(x^{2}+y^{2}=225\)