Answer :
Know that the equation for a circle is:
(x - h)² + (y - k)² = r²
where (h, k) is the coordinate for the center and r = radius
Factor into a perfect square for x and y by adding/subtracting grouping constants.
Given equation:
x² + y² - 4x - 8y - 5 = 0
going to group all x terms together and add +4 to both sides to give a perfect square of x. This number is determined by taking the square of half the middle term coefficient. [-4x is middle term. (-4/2)² = 4]
(x² - 4x + 4) - 8y + y² - 5 = 4
(x - 2)² + y² - 8y - 5 = 4
Now for y-terms, (-8/2)² = 16
add 16 to both sides.
(x - 2)² + (y² - 8y + 16) - 5 = 4 + 16
(x - 2)² + (y - 4)² - 5 = 20
now add that 5 over.
final equation for circle:
(x - 2)² + (y - 4)² = 25
center is (2,4) and radius is 5
(x - h)² + (y - k)² = r²
where (h, k) is the coordinate for the center and r = radius
Factor into a perfect square for x and y by adding/subtracting grouping constants.
Given equation:
x² + y² - 4x - 8y - 5 = 0
going to group all x terms together and add +4 to both sides to give a perfect square of x. This number is determined by taking the square of half the middle term coefficient. [-4x is middle term. (-4/2)² = 4]
(x² - 4x + 4) - 8y + y² - 5 = 4
(x - 2)² + y² - 8y - 5 = 4
Now for y-terms, (-8/2)² = 16
add 16 to both sides.
(x - 2)² + (y² - 8y + 16) - 5 = 4 + 16
(x - 2)² + (y - 4)² - 5 = 20
now add that 5 over.
final equation for circle:
(x - 2)² + (y - 4)² = 25
center is (2,4) and radius is 5
