Circles in Standard Form

Show your work for each problem.

1.
What is the center of the circle ?
1. a)
2. b)
3. c)
4. d)
Answer:
The standard form is . Here, and , so the center is .
2.
What is the radius of the circle ?
1. a)
2. b)
3. c)
4. d)
Answer:
Since , we take the square root to find .
3.
A circle has equation . What is the radius?
Answer: 6
The equation shows . Taking the square root: .
4.
What is the center of the circle ?
1. a)
2. b)
3. c)
4. d)
Answer:
means . Similarly, means . Center: .
5.
What is the y-coordinate of the center of ?
Answer: -8
, so . The y-coordinate of the center is .
6.
Write the equation of a circle with center and radius . Enter only value.
Answer: 25
With center and radius : . So .
7.
A circle has center and radius . What is the equation?
1. a)
2. b)
3. c)
4. d)
Answer:
simplifies to .
8.
Find the center and radius of .
Answer: (-6, 1), 10
1. What is the x-coordinate of the center (h)? -6
2. What is the y-coordinate of the center (k)? 1
3. What is ? 100
4. What is the radius r? 10
9.
Write the equation of a circle with center and radius .
Answer: (x + 2)^2 + (y - 5)^2 = 16
1. What expression represents for h = -2? (x + 2)^2
2. What expression represents for k = 5? (y - 5)^2
3. What is when ? 16
4. Write the complete equation. (x + 2)^2 + (y - 5)^2 = 16
10.
Which point lies ON the circle ?
1. a)
2. b)
3. c)
4. d)
Answer:
Check : ✓. The other points don't satisfy the equation.
11.
A circle has center and passes through . Find the radius.
Answer: 5
1. What is the difference in x-coordinates? (4 - 1) 3
2. What is the difference in y-coordinates? (1 - (-3)) 4
3. What is ? 25
4. What is the radius (square root of your answer)? 5
12.
If a circle has equation , what is its diameter?
Answer: 12
, so . Diameter .
13.
Write the equation of a circle with center that passes through .
Answer: x^2 + (y + 4)^2 = 25
1. Calculate 9
2. Calculate 16
3. What is ? 25
4. Write the equation with center and x^2 + (y + 4)^2 = 25
14.
Point lies on a circle centered at the origin. What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
. (This is a 5-12-13 right triangle!)
15.
Is the point inside, on, or outside the circle ?
Answer: inside
1. Calculate 1
2. Calculate 4
3. What is the sum of these values? 5
4. Is 5 less than, equal to, or greater than 9? (inside/on/outside) inside