Equation of circle with center (0, 0) :
x2 + y2 = r2
Equation of circle with center (h, k) :
(x - h)2 + (y - k)2 = r2
Distance between center and point on the circle = radius
Midpoint of endpoints of diameter = center
Area of circle = πr2
Circumference of circle = 2πr
Problem 1 :
Ends of diameter : (-17, -9) and (-19, -9).
Solution :
Where (h, k) = -18, -9
(x - h)2 + (y - k)2 = r2
(x + 18)2 + (y + 9)2 = r2 --- (1)
(-17, -9) substitute the equation (1).
(-17 + 18)2 + (-9 + 9)2 = r2
12 = r2
r2 = 1 substitute the equation (1).
(x + 18)2 + (y + 9)2 = 1
Problem 2 :
Ends of diameter : (-3, 11) and (3, -13).
Solution :
Where h = 0 and k = -1
(x - h)2 + (y - k)2 = r2
(x - 0)2 + (y + 1)2 = r2
x2 + (y + 1)2 = r2--- (1)
(3, -13) substitute the equation (1).
32 + (-13 + 1)2 = r2
9 + (12)2 = r2
153 = r2
r2 = 153 substitute the equation (1).
x2 + (y + 1)2 = 153
Problem 3 :
Center : (-15, 3√7), Area : 2π
Solution :
Equation of circle with center (h ,k) :
(x - h)2 + (y - k)2 = r2
h, k is -15, 3√7
(x + 15)2 + (y - 3√7)2 = r2 --- (1)
Area of the circle = πr2
2π = πr2
r2 = 2
r2 = 2 substitute the equation (1).
(x + 15)2 + (y - 3√7)2 = 2
Problem 4 :
Center : (-11, -14), Area : 16π
Solution :
Equation of circle with center (h ,k) :
(x - h)2 + (y - k)2 = r2
Where h = -11 and k = -14
(x + 11)2 + (y + 14)2 = r2 --- (1)
Area of the circle = πr2
16π = πr2
r2 = 16
r2 = 16 substitute the equation (1).
(x + 11)2 + (y + 14)2 = 16
Problem 5 :
Center : (-5, 12), Circumference : 8π
Solution :
Equation of circle with center (h ,k) :
(x - h)2 + (y - k)2 = r2
Where h = -5 and k = 12
(x + 5)2 + (y - 12)2 = r2 --- (1)
Area of the circle = 2πr
8π = 2πr
r = 4
r = 4 substitute the equation (1).
(x + 5)2 + (y - 12)2 = 42
(x + 5)2 + (y - 12)2 = 16
Problem 6 :
Center : (15, 14), Circumference : 2π√15
Solution :
Equation of circle with center (h ,k) :
(x - h)2 + (y - k)2 = r2
Where h = 15 and k = 14
(x - 15)2 + (y - 14)2 = r2 --- (1)
Area of the circle = 2πr
2π√15 = 2πr
r = √15
r = √15 substitute the equation (1).
(x - 15)2 + (y - 14)2 = (√15)2
(x - 15)2 + (y - 14)2 = 15
Problem 7 :
Center : (2, -5), Point on circle : (-7, -1)
Solution :
Equation of circle with center (h ,k) :
(x - h)2 + (y - k)2 = r2
Where h = 2 and k = -5
(x - 2)2 + (y + 5)2 = r2 --- (1)
Point on circle r = √[(x2 - x1)2 + (y2 - y1)]
(x1, y1) = (2, -5)
(x2, y2) = (-7, -1)
= √[(-7 - 2)2 + (-1 + 5)2]
= √[(-9)2 + (4)2]
= √[81 +16]
r = √97
r = √96 substitute the equation (1).
(x - 2)2 + (y + 5)2 = (√96)2
(x - 2)2 + (y + 5)2 = 97
Problem 8 :
Center : (14, 17), Point on circle : (15, 17)
Solution :
Equation of circle with center (h ,k) :
(x - h)2 + (y - k)2 = r2
Where h = 14 and k = 17
(x - 14)2 + (y - 17)2 = r2 --- (1)
Point on circle r = √[(x2 - x1)2 + (y2 - y1)2]
(x1, y1) = (14, 17)
(x2, y2) = (15, 17)
= √[(15 - 14)2 + (17 - 17)2]
= √(1)2
r = 1
r = 1 substitute the equation (1).
(x - 14)2 + (y - 17)2 = 12
(x - 14)2 + (y - 17)2 = 1
Problem 9 :
Center : (-11, -8), Radius : 4
Solution :
Center of the circle is (x - h)2 + (y - k)2 = r2
Where h = -11 and k = -8
(x + 11)2 + (y + 8)2 = 42
(x + 11)2 + (y + 8)2 = 16
Problem 10 :
Center : (-6, -15), Radius : √5
Solution :
Center of the circle is (x - h)2 + (y - k)2 = r2
h, k is -6, -15
(x + 6)2 + (y + 15)2 = (√5)2
(x + 6)2 + (y + 15)2 = 5
Problem 11 :
Solution :
By observing the figure,
Center : (0, 3)
Radius : 3
Center of the circle is (x - h)2 + (y - k)2 = r2
Where h = 0 and k = 3
(x - 0)2 + (y - 3)2 = 32
x2 + (y - 3)2 = 9
Problem 12 :
Solution :
By observing the figure,
Center : (4, -3)
Radius : 1
Center of the circle is (x - h)2 + (y - k)2 = r2
Where h = 4 and k = -3
(x - 4)2 + (y + 3)2 = 12
(x - 4)2 + (y + 3)2 = 1
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM