# Solutions to Exercises on Equation of Circle

We present the solutions to the exercises in Tutorial on Equation of Circle with explanations.

### Matched Exercise 1

Find the equation of a circle whose center is at (2 , - 4) and radius 3.

(x - 2)
2 + (y + 4)2 = 9

### Matched Exercise 2

Find the equation of a circle that has a diameter with the endpoints given by A(0 , -2) and B(0 , 2).

### Solution to Matched Exercise 2

center at (0 , 0)
equation: x
2 + y2 = 4

### Matched Exercise 3

Find the center and radius of the circle with equation
x
2 - 2x + y2 - 8y + 1 = 0

### Solution to Matched Exercise 3

write the given equation in standard form by completing the squares.
(x - 1)
2 + (y - 4)2 = 42
center at (1 , 4).

### Matched Exercise 4

Is the point P(-1, -3) inside, outside or on the circle with equation
(x - 1)
2 + ( y + 3)2 = 4

### Matched Exercise 4

center is at (1 , -3) and radius is equal to 2.
distance d from center to the point (-1 , -3) is given by
d = sqrt[(-1 - 1)
2 + (-3 + 3)2]
= 2
Distance d is equal to the radius of the circle. Point P is on the circle.