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.

Solution to Matched Exercise 1


(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)
radius = 2
equation: x2 + y2 = 4

Matched Exercise 3

Find the center and radius of the circle with equation
x2 - 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
radius = 4
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.