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MAC Project 2233
1. What do we call the set of all points whose distance from the point ( h, k ) is r? Derive an
equation for the graph using distance formula.
Rewrite the following equations of circles by completing squares, draw the graphs, and label
the points of intersection A and B . What is the distance between the centers of the circles?
What is the slope of the line through the two centers?
x2 + y 2 2 x + 2 y 8 = 0
x2 + y 2 6 x 4 y + 8 = 0
2. When the brightness x of a light source is increased, the eye reacts by decreasing the area R
of the pupil. The experimental formula
40 + 24x2/5
R=
1 + 4x2/5
has been used to model the of dependence R on x, where R is measured in square millimeters
and x 0 is measured in appropriate units of brightness.
Should the pupil have a larger area when x = 0 or when x = 32 ? How may times larger is it?
The equation above can be solved for the variable x2/5 . Show that x =
R 40
24 4R
5/2
. For
what x-value will R be 10 square millimeters (round to the nearest tenth)?
Note that x is not a real number for some R values because of the square root. Solve an
inequality in order to determine the values of R for which there is a real solution ( x, R ).
What seem to be the smallest and largest possible areas R for the pupil?