1. the equation of a circle is x ^2 + y ^2 – 4 x + 2 y = 11 . what are the coordinates of the center of the circle? question 1 options (2, –1) (4, –2) (–4, 2) (–2, 1) 2. what is the equation of the circle with center (4, -3) and radius 2? question 2 options: (x + 4)^2 + (y – 3)^2 = 4 (x + 4)^2 – (y – 3)^4 = 4 (x – 4)^2 + (y + 3)^2 = 2 (x – 4)^2 + (y + 3)^2 = 4 3. what is the equation of this circle? (has picture) (x – 2)^2 + (y – 7)^2 = ½ (x + 2)^2 + (y + 7)^2 = ¼ (x + 7)^2 + (y + 2)^2 = ¼ (x + 2)^2 + (y + 7)^2 = ½ 4. what are the center and radius of the circle described by the equation x2 + y2 – 18x + 12y + 68 = 0? question 4 options: center (-9, 6); radius 7 center (9, -6); radius 7 center (-6, 9); radius 7 center (6, -9); radius 7 5. select the equation of a circle with center (-3, 7) and radius 5. question 5 options: (x - 3)^2 + (y + 7)^2 = 25 (x + 3)^2 + (y - 7)^2 = 25 (x + 3) + (y - 7) = 25 (x - 3) + (y + 7) = 25

Problem 1

x^2 + y^2 - 4x + 2y = 11
x^2 - 4x + y^2 + 2y = 11
(x^2 - 4x) + (y^2 + 2y) = 11
(x^2 - 4x + 4) + (y^2 + 2y) = 11 + 4
(x - 2)^2 + (y^2 + 2y) = 15
(x - 2)^2 + (y^2 + 2y + 1) = 15+1
(x - 2)^2 + (y + 1)^2 = 16

The equation
(x - 2)^2 + (y + 1)^2 = 16
can be written as
(x - 2)^2 + (y - (-1))^2 = 4^2
which is in the form
(x-h)^2 + (y-k)^2 = r^2
where,
center = (h,k) = (2,-1)
radius = r = 4

Choice A) (2,-1)


Problem 2

Given Center = (h,k) = (4,-3)
h = 4, k = -3
Given Radius = r = 2

(x-h)^2 + (y-k)^2 = r^2
(x-4)^2 + (y-(-3))^2 = 2^2
(x-4)^2 + (y+3)^2 = 4

Answer is choice D


Problem 3

Based on the picture, the center is (-2,-7)
(h,k) = (-2,-7)
h = -2
k = -7

Each tick mark is 1/2 a unit. The distance from the red center to the outer edge of the circle is 1 tick or 1/2 a unit. The radius is 1/2 a unit. So r = 1/2 and r^2 = (1/2)^2 = 1/4

(x-h)^2 + (y-k)^2 = r^2
(x-(-2))^2 + (y-(-7))^2 = (1/2)^2
(x+2)^2 + (y+7)^2 = 1/4

Answer is choice B


Problem 4

x^2 + y^2 - 18x + 12y + 68 = 0
(x^2 - 18x) + (y^2 + 12y) + 68 = 0
(x^2 - 18x + 0) + (y^2 + 12y + 0) + 68 = 0
(x^2 - 18x + 81 - 81) + (y^2 + 12y + 36 - 36) + 68 = 0
(x^2 - 18x + 81) - 81 + (y^2 + 12y + 36) - 36 + 68 = 0
(x - 9)^2 + (y + 6)^2 - 81 - 36 + 68 = 0
(x - 9)^2 + (y + 6)^2 - 49  = 0
(x - 9)^2 + (y + 6)^2 = 49
(x - 9)^2 + (y - (-6))^2 = 7^2

The center is (9,-6) and the radius is 7


Problem 5

Center = (h,k) = (-3,7)
Radius = r = 5

(x-h)^2 + (y-k)^2 = r^2
(x-(-3))^2 + (y-7)^2 = 5^2
(x+3)^2 + (y-7)^2 = 25

Answer is choice B