Question

what is the radius of the circle with the equation $(x - 2)^2+(y + 1)^2 = 4$?

1. a.
2. b.
3. c.
4. d.

which of the following points lies on the circle with equation $(x - 4)^2+(y + 2)^2 = 36$?
a. $(4,8)$
b. $(4,-2)$
c. $(4,4)$
d. $(0,2)$

Explanation:

Step1: Recall the standard form of a circle equation

The standard form of a circle 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

For the equation \((x - 2)^2+(y + 1)^2 = 4\), we have \(r^2=4\).

Step3: Solve for \(r\)

Take the square root of both sides: \(r=\sqrt{4}=2\).

Answer:

b. 2