x^2-10x+y^2=k is ta circle tangent to the y-axis for what real number k?
complete the square to find the centre
x^2 -10x + 25 + y^2 = k + 25
(x-5)^2 + y^2= k+25
so the centre must be (5,0), which lies on the x-axis
to be tangent to the y-axis it must pass through (0.0)
and its radius must be 5
so the equation must be
(x-5)^2 + y^2 = 25
and k+25 must equal 25
so k = 0