ok so here's the Q i am stuck on

1) Find the equations of all tangents to the graph of f(x) = x^2 - 4x + 25 that passes through the origin (0,0)

so from my understanding, the tangent line has to pass through the origin

y = mx + b

sub in (0,0) gives me b = 0 (makes sense since line isnt shifted and only the slope is something diff)

so then i differentiate the f(x)

and get f'(x) = 2x-4, which is the slope

then i sub that back into my line equation

y = (2x-4)x + b

y = 2x^2 -4x +b

0 = 2x^2 -4x

solving for x i get x = 2, x = 0

up until here i am wondering if i did this correctly

and if i did, how do i now write the equation of the tangents down?

y = 2x + b AND y = b

??

thanks in advance