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Mathematics-Online problems: | ||
Solution to the problem of the (previous) week |
Problem:
The figure shows the parabola
Find the parameter as well as the point of tangency
and the point of intersection
.
Answer:
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(The results should be correct to four decimal places.)
Solution:
Equating the slopes at the point of tangency, we obtain
Hence, we have
Simplifying, we get and
, which yields
Substitute in the equation of the parabola to find the intersection point:
Since is a zero of order 2 of
(
-coordinate of the point of tangency), we can factor
and obtain the form