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 \( (x - 1)^2 + ( y + 3)^2 = 4 \)?
Solution to 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.
