Question

1. what is the radius of the circle with the equation ((x + 3)^2 + (y - 2)^2 = 36)?

a. 6
b. 9
c. 12
d. 3

Explanation:

Step1: Recall circle equation formula

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 given equation

Given equation: \((x + 3)^2 + (y - 2)^2 = 36\). Here, \(r^2 = 36\).

Step3: Solve for radius \(r\)

Take the square root of both sides: \(r=\sqrt{36}=6\).

Answer:

a. 6