Question

1. - / 1 points give an equation of the circle with its center at the origin and a radius of 5 units.

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: Identify center and radius values

The center is at the origin \((0,0)\), so \(h = 0\) and \(k = 0\), and \(r = 5\).

Step3: Substitute values into formula

Substitute \(h = 0\), \(k = 0\), and \(r = 5\) into \((x - h)^2+(y - k)^2=r^2\), we get \((x - 0)^2+(y - 0)^2=5^2\), which simplifies to \(x^{2}+y^{2}=25\).

Answer:

\(x^{2}+y^{2}=25\)