Question

what is the radius of the circle given by the equation below? (x + 1)^2 + (y + 9)^2 = 36 a. 10 b. 18 c. 36 d. 6

Explanation:

Step1: Recall the standard circle equation

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

Step2: Compare with the given equation

Given \((x + 1)^2+(y + 9)^2=36\). We can rewrite \(36\) as \(6^2\). So, \(r^2 = 36\).

Step3: Solve for \(r\)

Take the square root of both sides: \(r=\sqrt{36}\). Since radius \(r>0\), \(r = 6\).

Answer:

D. 6