Tangent at Point Q?

Question

I'm given the information that line L is tangent to the graph of y = x^2/500 at the point Q.
a. Find the x-coordinate of point Q.
b. Write an equation for the line L.
c. suppose the graph of y represents a hill. There is a 50 foot tree growing vertically at the top of the hill. Does a spotlight at point P directed along line L shine on any part of the tree?

Answer 1

Remember that the derivative gives you the slope of a tangent line. So for y = (x^2)/500, you have dy/dx = 2x/500, or x/250.

a) You need more information, because Q could be anywhere on the graph, since you can draw a line tangent to the graph at any point.

b) You have the slope of the line, so if you knew the x-coordinate of Q from #1, you could plug it into y = (x^2)/500 to find the y-coordinate. This (x,y) point has to be on the line L too, so now knowing the slope and a point, you could determine an equation for the line

c) Depends on where "P" is.

Answer 2

there is no information about L and P.
The graph of y is a parabola with its vertix at (0,0).
To give you an answer more information is needed