Answer:
centre = (4, - [tex]\frac{11}{2}[/tex] )
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
x² + y² - 8x + 11y - 2 = 0 ( collect terms in x and y together and add 2 to both sides )
x² - 8x + y² + 11y = 2
using 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([tex]\frac{11}{2}[/tex] )y + [tex]\frac{121}{4}[/tex] = 2 + 16 + [tex]\frac{121}{4}[/tex]
(x - 4)² + (y + [tex]\frac{11}{2}[/tex] )² = [tex]\frac{193}{4}[/tex] ← in standard form
with centre (4, - [tex]\frac{11}{2}[/tex] )
