Question

Does the equation x^2-6x+y^2-6y =-9 intersects the y-axis

Answer 1

Intersecting the y axis means x is o, so you plug x=0 in the equation and solve for y. if y has real solutions, then the answer is yes.
Let's find out:
0+y^2-6y=-9
y^2-6y+9=0
(y-3)(y-3)=0
y=3
3 is a real number, so yes, the equation intersects the y axis at (0,3)