Question

question 6: standard g.gpe.1
which of the following shows the equation for a circle with center (2,1) and radius of 2?
a. (x-3)² + (y-9)² = 2
b. (x-2)² + (y-1)² = 4
c. (x-2)² + (y-2)² = 2
d. (x-1)² + (y-2)² = 2

question 7: standard g.gpe.1
which of the following shows the equation for a circle with center (3,8) and radius of 5?
a. (x-5)² + (y-3)² = 8
b. (x-3)² + (y-8)² = 25
c. (x-5)² + (y-5)² = 3
d. (x-8)² + (y-3)² = 25

for questions 8-10 use the following graph. the green point is the center of the circle.
graph of a circle with center at (2,2) on a grid

question 8: standard g.gpe.1
the center of the circle is at....
a. (1,2)
b. (2,1)
c. (3,3)
d. (1,3)

question 9: standard g.gpe.1
the radius of the circle is...
a. 4
b. 1
c. 5
d. 2

Explanation:

Question 6

Step1: Recall the circle equation formula

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

Step2: Identify \(h\), \(k\), and \(r\)

Given center \((2,1)\), so \(h = 2\), \(k = 1\), and radius \(r = 2\), then \(r^2 = 4\).

Step3: Substitute into the formula

Substituting \(h = 2\), \(k = 1\), and \(r^2 = 4\) into the formula, we get \((x - 2)^2 + (y - 1)^2 = 4\), which matches option b.

Step1: Recall the circle equation formula

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

Step2: Identify \(h\), \(k\), and \(r\)

Given center \((3,8)\), so \(h = 3\), \(k = 8\), and radius \(r = 5\), then \(r^2 = 25\).

Step3: Substitute into the formula

Substituting \(h = 3\), \(k = 8\), and \(r^2 = 25\) into the formula, we get \((x - 3)^2 + (y - 8)^2 = 25\), which matches option b.

Step1: Analyze the graph

From the graph, the green point (center) has an \(x\)-coordinate of 1 (since it's at \(x = 1\) on the grid) and a \(y\)-coordinate of 2 (at \(y = 2\) on the grid). So the center is \((1,2)\), which matches option a.

Answer:

b. \((x - 2)^2 + (y - 1)^2 = 4\)

Question 7