# Calculus and Conics

1. Mar 4, 2012

### bmr676

1. The problem statement, all variables and given/known data
A cross-section of a parabolic reflector is shown in the figure. The bulb is located at the focus and the opening at the focus is 10 cm. Find an equation of the parabola where V is at the origin. Find the diameter of the opening | CD |, 7 cm from the vertex.

Because the picture is not on here as well, it should be mentioned that the focus is closer to the vertex than 7cm. Also, it is labeled that the 10cm opening at the focus is from point A to B.

2. Relevant equations
x=ay2

3. The attempt at a solution
At the focus, the coordinates are (x,5) and (x,-5) for A and B respectively. Vertex coordinates are (0,0). Equation is x=a(y^2), thus at the focus, the equation is x=25a. Also, the points C and D are (7,y) and (7,-y) respectively. So the equations for those would be 7=a(y^2).

I feel that not enough information was not given with this problem, but I must be missing something. Any inputs?