Answer:
see explanation
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
Given
16 + x² + y² - 8x - 6y = 0 ( subtract 16 from both sides )
x² + y² - 8x - 6y = - 16 ( collect x and y terms together )
x² - 8x + y² - 6y = - 16
Use the method of completing the square
add ( half the coefficient of the x/y terms)² to both sides
x² + 2(- 4)x + 16 + y² + 2(- 3)y + 9 = - 16 + 16 + 9
(x - 4)² + (y - 3)² = 9 ← in standard form
with centre (4, 3 ) and r = [tex]\sqrt{9}[/tex] = 3
This is a circle with centre (4, 3 ) and radius 3
