Answer:
y = 5
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 ad r is the radius
Given
x² + y² - 10y + 18x = 2 ( Rearrange collecting x and y terms together )
x² + 18x + y² - 10y = 2
Using the method of completing the square
add ( half the coefficient of the x/ y term )² to both sides
x² + 2(9)x + 81 + y² + 2(- 5)y +25 = 2 + 81 + 25
(x + 9)² + (y - 5)² = 108 ← in standard form
with centre = (- 9, 5 )
The y- coordinate of the centre is therefore y = 5
