Higher Maths Differentiation Help?

the answer is (a) (4,8)

the point (3,9) is on the curve therefore it satisfies the equation y = (x - 4)^2 + k so sub it in

9 = (3-4)^2 + k

9 = (-1)^2 + k

k + 1 = 9

k = 8 .. the curve now has the equation

y = (x-4)^2 + 8

y = x^2 - 8x + 24 ...... differentiate this

dy/dx = 2x - 8 .. as the point is stationary (slope = 0)

2x - 8 = 0

x = 4 ... this is the x-value of the co-ordinate .. sub this in to the equation of the curve and solve for y

y = (4)^2 - 8(4) + 24

y = 16 - 32 + 24

y = 40 - 32

y = 8

Co- ordinate of stationary point is (4,8)

The answer I think is B

Substitute (3,9) into y=mx+c

Make the gradient 0 as its stationary

So 9=0*3+c so 9=c

So y=0+9

Y=9

The y coordinate of the points is 9,

B is the only answer where that is true

Hope this makes sense??