Word problem. Y=0.0015x^(2)+C. Line tangent to the curve is given by Y= 0.3x -10. C=?

[Kamhogo]

" The cable of a 200m suspension bridge can be represented by y= 0.0015x^(2) +C.
At one point,the tension is directed along the line y= 0.3x -10. Find the value of C."

Can you please give me a hint as of how to begin? Or just explain the question more simply.
Thanks!

 

[Deleted member 4993]

" The cable of a 200m suspension bridge can be represented by y= 0.0015x^(2) +C.
At one point,the tension is directed along the line y= 0.3x -10. Find the value of C."

Can you please give me a hint as of how to begin? Or just explain the question more simply.
Thanks!

The tension at a point is directed along the tangent a that point.

What is the slope of tangent to the given curve at (x_o, y_o)?

 

[Kamhogo]

If x=0, then f (0) = 0.0015 (0)^(2) +C = C

Slope of tangent line to the curve at (0,0) = f'(0) = 0.003 (0) = 0 = m

Equation of tangent line ==> (Y-Yo) = m ( X-Xo)
Y -C = m ( X -0) = 0
Y = C

I'm a little bit confused because f (x) = 0. 0015x^(2) + C has no point at (0,0) unless C = 0, which is not the case ( textbook answer is 5). I also have the intuition that I can somehow have to equate y= 0.3x -10 with something and from there solve for C but I can't seem to find how...