Question

what is the radius of the circle x² + y² = 49? simplify any fractions.

Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle centered at the origin \((0,0)\) is \(x^{2}+y^{2}=r^{2}\), where \(r\) is the radius.

Step2: Compare given equation with standard form

Given \(x^{2}+y^{2}=49\), and since \(49 = 7^{2}\), we have \(r^{2}=49\).

Step3: Solve for \(r\)

Taking the square - root of both sides, \(r=\sqrt{49}\). Since \(r>0\) (radius is a non - negative quantity), \(r = 7\).

Answer:

7