# Circles

# Circles on the Coordinate Plane Exercises

### Example 1

Give an equation for the circle with center (6, 8) and radius 12 units.

### Example 2

Give an equation for the circle with center (-3, -25) and radius 169 units.

### Example 3

Give an equation for the circle with center (-22.3, 7.95) and radius 4.4 units.

### Example 4

What are the center and radius of the circle with equation (x – 13)^{2} + (*y* + 45)^{2} = 81?

### Example 5

What are the center and radius of the circle with equation (*x* + 78)^{2} + (*y* + 13)^{2} = 2?

### Example 6

What are the center and radius of the circle with equation (x + 6)^{2} + (*y* – 4.3)^{2} = 169?

### Example 7

Given the circle with equation (*x* – 21)^{2} + (*y* + 18)^{2} = 36, is the point (24, -12) in the exterior of the circle, in the interior of the circle, or on the circle?

### Example 8

Given the circle with equation (*x* + 4)^{2} + (*y* – 58)^{2} = 100, is the point (-14, 60) in the exterior of the circle, in the interior of the circle, or on the circle?

### Example 9

Given the circle with equation (*x* – 9)^{2} + (*y* – 3)^{2} = 15^{2} , is the point (6, 5) in the exterior of the circle, in the interior of the circle, or on the circle?

### Example 10

Given the circle with equation (*x* – 101)^{2} + (*y* – 45)^{2} = 61^{2} , is the point (90, 105) in the exterior of the circle, in the interior of the circle, or on the circle?

### Example 11

Find an equation for the line that is tangent to the circle with equation (*x* – 15)^{2} + (*y* + 22)^{2} = 17^{2} at the point (23, -7).

### Example 12

Find an equation for the line that is tangent to the circle with equation (*x* + 2)^{2} + (*y *+ 40)^{2} = 37^{2} at the point (10, -5).