2011 Fall Calc. I Math. Phys. Sci. (Math 151) Sect. 01,02,03
1
Workshop 5 — Hint for Problem 3
Thursday October 13
Humberto can see two mathematically correct ways of solving this problem. Both rely on
Fguring out a mathematical characterization of a circle that is ‘too big’ to be inside the parabola.
Quite possibly there are other ways – perhaps better ways – of solving this problem correctly.
Solution 1 hint.
The key idea for this approach is to realize that a circle is too big if and
only if it has points of intersection with the parabola, other than the origin. Take any positive
number
r
. Write the equation of the circle that has radius
r
, that has its center on the positive
y
axis and that is tangent to the
x
axis. If you do not remember the equation of a circle, look it
up in the book or in the internet. (You should know this equation by memory, or know how to
derive it.) Armed with the equation of this circle of radius
r
, determine whether it has any points
of intersection with the parabola other than the origin. After some work, you should be able to
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 Fall '11
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