1. ## Conic Sections

We are covering conic sections, including circles, parabolas, ellipses, and hyperbolas in pre-calculus. We were given a worksheet and there is one problem I just can't seem to grasp. here it is:

Two suppliers, supplier 1 and supplier 2, are located at (0,0) and (6,0) respectively. They both charge $10 per mile (1 unit being a mile) for shipping their goods. In addition to the shipping cost, supplier 1 charges$980 for buying his goods and supplier 2 charges $1000 for his goods. Find a set of points (x,y) for which the total cost (shipping plus goods) is the same for both suppliers. 2. You need to find the points of intersection of the two circles. The circle with center at$\displaystyle (0,0)$has radius$\displaystyle r_1$, the circle with center at$\displaystyle (6,0)$has radius$\displaystyle r_2$. Since supplier 1 charges$20 less than supplier 2, $\displaystyle r_2 = r_1-2$ describes the relationship between their radii such that the total cost is the same from each.

The equations of the two circles are:
$\displaystyle x^2+y^2=r_1^2$

$\displaystyle (x-6)^2+y^2=r_2^2=(r_1-2)^2$

Combine the two equations, and find the radical line to describe the set of points you're looking for.
Circle-Circle Intersection -- from Wolfram MathWorld

Some of the points you will find (if I did my math right):
$\displaystyle (4,0)$ at $\displaystyle r_1=4$
$\displaystyle \{(6,8), (6,-8)\}$ at $\displaystyle r_1=10$
$\displaystyle \{(20,48), (20,-48)\}$ at $\displaystyle r_1=52$
$\displaystyle \{(102,280), (102,-280)\}$ at $\displaystyle r_1=298$