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: x^{2} + y^{2} = 4

Matched Exercise 3

Find the center
and radius of the circle with equation
x^{2} - 2x + y^{2} - 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} = 4^{2}
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.