Question

which is the standard equation for a circle centered at the origin with radius r?
a. x + y = r
b. x² = y² + r²
c. x² + y² = r
d. x² + y² = r²

Explanation:

Step1: Recall circle equation formula

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

Step2: Substitute center at origin

Since the center is at the origin \((0,0)\), \(h = 0\) and \(k = 0\). Substituting these values into the formula \((x - h)^2+(y - k)^2=r^2\), we get \((x - 0)^2+(y - 0)^2=r^2\), which simplifies to \(x^{2}+y^{2}=r^{2}\).

Answer:

D. \(x^{2}+y^{2}=r^{2}\)