Question

what is the radius of a circle whose equation is $(x - 7)^{2}+(y - 10)^{2}=4$?
2 units
4 units
8 units
16 units

Explanation:

Step1: Recall the standard form of a circle's equation

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

Step2: Compare the given equation with the standard form

Given equation \((x - 7)^2+(y - 10)^2 = 4\). Comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(r^2 = 4\).

Step3: Solve for \(r\)

Take the square root of both sides: \(r=\sqrt{4}\). Since radius \(r>0\), \(r = 2\).

Answer:

2 units