Answers to Exercises on Equation of Circle






We present the answers to the exercises in Tutorial on Equation of Circle.

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

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.






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