Examples Of Circles

5 SOLVED PROBLEMS OF CIRCLE

EXAMPLE# 1

Find the center and radius of this circle:

x² + y² – 8x + 2y – 19 = 0

SOLUTION:

x² – 8x + 16 + y² + 2y + 1 = 19+16+1

(x – 4)² + (y + 1)² = ⎷36

(x – 4)² + (y + 1)² = 6²

Center: (4,-1) Radius: r = 6
GRAPH:

EXAMPLE#2

What is the center and radius of the

circle indicated by this equation?

(x – 2)² + (y)² = 36

SOLUTION:

(x – 2)² + (y)² = ⎷36

(x – 2)² + (y)² = 6²

Center: (2,0) Radius: r = 6

GRAPH:

EXAMPLE#3

What is the equation of the circle

with a center at (4,-5) and a point

in the circle at (4,-2).What is the

radius?

SOLUTION:

(x-h)² + (y-k)² = r² Standard Formula

(x-4)² + (y-(-5))² = r² 

(4-4)² + (-2+5)² = r²

(0)² + (3)² = r²

9 = r²

r = 3²

^GRAPH:

Center: (4,-5) Radius: r = 3

EXAMPLE#4

Determine the center and the radius

Of the circle from this equation and graph

x² + y² – 8x + 6y + 9 = 0

SOLUTION:

x² – 8x + 16 + y² + 6y + 9 = -9 + 9 + 16

(x-4)² + (y+3)² = 16

(x-4)² + (y+3)² = 16

(x-4)² + (y+3)² = 4²

Center: (4,-3) Radius: r = 4

GRAPH:

EXAMPLE#5

Determine the center and the radius

Of the circle from this equation and

graph

x² + y² – 6x + 6y – 18 = 0

x² – 6x + 9 + y² + 6y + 9 = 18 + 9 + 9

(x-3)² + (y+3)² = 36

(x-3)² + (y+3)² = 36

(x-3)² + (y+3)² = 6²

Center: (3,-3) Radius: r = 6

GRAPH: