Answer:
The center of the circle = (3, 1)
The radius of a circle is given as r = √6
Explanation:
The equation of a circle is given as:
( x - a)² + (y - b)² = r²
where ( a , b) = center of the circle
r = radius of the the circle
In the question above, we are given the equation of a circle as
x² + y² - 6x - 2y + 4= 0
In order to find the center and radius of this circle we would use completing the square method to solve it
Step 1
Collect the like terms
x² - 6x + y² - 2y + 4= 0
Step 2
Complete the square for both x and y
x² - 6x + (-6/2)² + y² - 2y + (-2/2)² = - 4 +(- 6/2)² + (-2/2)²
x² - 6x + (-3)² + y² - 2y + (-1)² = -4 + (3)² + (1)²
x² - 6x + 9 + y² - 2y + 1 = -4 + 9 + 1
(x² - 6x + 9) + (y² - 2y + 1 )= -4 + 9 + 1
(x² - 3x - 3x +9) + ( y² - y - y +1) = 6
x(x - 3) -3( x - 3) + y( y - 1) - 1( y - 1) = 6
(x - 3) (x -3) +(y - 1) ( y - 1) = 6
(x - 3)²(y - 1)² = 6
Since,
The equation of a circle is given as:
( x - a)² + (y - b)² = r²
where ( a , b) = center of the circle
r = radius of the the circle
The equation of the the circle for the above question is calculated as:
(x - 3)²(y - 1)² = 6
where ( a , b) = center of the circle = (3, 1)
r = radius of the the circle
r² = 6
r = √6