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: x 2 + y 2 = 4
Matched Exercise 3
Find the center and radius of the circle with equationx 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.