Question

The point (-3,2) lies on a circle whose equation is (x + 3)^2 + (y + 1 )^2 =r^2. Which of the following must be the radius of the circle?

Answer 1

1. 3

2. A

Explanation:

1. (-3+3)^2 + (2 + 1)^2 - r^2 = 0

0 + 9 - r^2 = 0

r^2 = 9

r = 3

2. 2x^2 + 4x + 2y^2 + 12y = - 6

Divide by 2.

(x^2 + 2x) + (y + 6y) = -3

Remember how to complete the square..

(b/2)^2

So...

(2/2) ^ 2 = 1

(6/2) ^ 2 = 9

(x^2 + 2x + 1) + (y^2 + 6y + 9) = -3 + 1 + 9 <--- You must remember to add whatever you add on the left to the right!

Now.. rewrite in standard form..

(x+1)^2 + (y+3)^2 = 7

Careful!! the circle equation is written as

(x - h)^2 + (y - h)^2 = r^2

Meaning that the radius is square root of 7. At center (-1, -3)