Give an equation for the circle with center (6, 8) and radius 12 units.
Hint
Look up the implicit formula for a circle.
Answer
(x – 6)2 + (y – 8)2 = 144
Example 2
Give an equation for the circle with center (-3, -25) and radius 169 units.
Hint
Look up the implicit formula for a circle.
Answer
(x + 3)2 + (y + 25)2 = 1692
Example 3
Give an equation for the circle with center (-22.3, 7.95) and radius 4.4 units.
Hint
Look up the implicit formula for a circle.
Answer
(x + 22.3)2 + (y – 7.95)2 = 4.42
Example 4
What are the center and radius of the circle with equation (x – 13)2 + (y + 45)2 = 81?
Hint
Look up the implicit formula for a circle.
Answer
Center: (13, -45); Radius: 9
Example 5
What are the center and radius of the circle with equation (x + 78)2 + (y + 13)2 = 2?
Hint
Look up the implicit formula for a circle.
Answer
Center: (-78, -13); Radius:
Example 6
What are the center and radius of the circle with equation (x + 6)2 + (y – 4.3)2 = 169?
Hint
Look up the implicit formula for a circle.
Answer
Center: (-6, 4.3); Radius: 13
Example 7
Given the circle with equation (x – 21)2 + (y + 18)2 = 36, is the point (24, -12) in the exterior of the circle, in the interior of the circle, or on the circle?
Hint
Remember that the left hand side of the equation tells us the square of the distance between any point (x, y) and the center of the circle.
Answer
Exterior
Example 8
Given the circle with equation (x + 4)2 + (y – 58)2 = 100, is the point (-14, 60) in the exterior of the circle, in the interior of the circle, or on the circle?
Hint
Remember that the left hand side of the equation tells us the square of the distance between any point (x, y) and the center of the circle.
Answer
Exterior
Example 9
Given the circle with equation (x – 9)2 + (y – 3)2 = 152 , is the point (6, 5) in the exterior of the circle, in the interior of the circle, or on the circle?
Hint
Remember that the left hand side of the equation tells us the square of the distance between any point (x, y) and the center of the circle.
Answer
Interior
Example 10
Given the circle with equation (x – 101)2 + (y – 45)2 = 612 , is the point (90, 105) in the exterior of the circle, in the interior of the circle, or on the circle?
Hint
Remember that the left hand side of the equation tells us the square of the distance between any point (x, y) and the center of the circle.
Answer
On the circle
Example 11
Find an equation for the line that is tangent to the circle with equation (x – 15)2 + (y + 22)2 = 172 at the point (23, -7).
Hint
The tangent line will be perpendicular to the radius of the circle at the point of tangency.
Answer
Example 12
Find an equation for the line that is tangent to the circle with equation (x + 2)2 + (y + 40)2 = 372 at the point (10, -5).
Hint
The tangent line will be perpendicular to the radius of the circle at the point of tangency.
