1. ## Calc Help!!!

A car is traveling at night along a highway shaped like a parabola with its vertex at the origin. The car starts at a point 100 m west and 100 m north of the origin and travels inan easterly direction. There is a statue located 100 m east and 50 m north of the origin. At what point on the highway will the car's headlights illuminate the statue?

what i have so far:
y'(x)=m=(50-y)/(100-x)
delta x=100-x
delta y=50-y
delta y=f(x+deltax)-f(x)
=50-y=100-x
y'=1
y=x-50

I dont no how to finish the problem off so and i feel like i am going in circles, so any help would be great! Thanks!!!!

2. What you must do is find at what point a line is tangent to the parabola and passes through (100,50).

You can use $\displaystyle y=a(x-h)^{2}+k$ to find your parabola equation.

You need to find the derivative of y to get the slope m.

In doing so, we find the equation is $\displaystyle y=\frac{1}{100}x^{2}$

Now, you have a 'passes through' point but do not know where it is tangent.

You can use $\displaystyle y-y_{1}=m(x-x_{1})$

$\displaystyle \underbrace{\frac{1}{100}x^{2}}_{\text{y}}-\overbrace{50}^{\text{y1}}=\underbrace{\frac{x}{50 }}_{\text{m}}\overbrace{(x-100)}^{\text{x-x1}}$

Now, solve for x. Only one answer will be within reason.