Difference between revisions of "1988 AIME Problems/Problem 14"
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== Solution == | == Solution == | ||
− | {{ | + | <math>bc=84</math> |
+ | |||
+ | We need to find a formula for <math>P^*</math> if <math>P=(x,y)</math>. | ||
+ | |||
+ | With some algebra, we find this to be: | ||
+ | |||
+ | <math>P^*=(\frac{-3x+4y}{5},\frac{4x+3y}{5})</math>. | ||
+ | |||
+ | Substituting in, we get: | ||
+ | |||
+ | <math>\frac{(-3x+4y)(4x+3y)}{25}=1</math> | ||
+ | |||
+ | Expanding, | ||
+ | |||
+ | <math>12x^2-7xy-12y^2+25=0</math>. | ||
+ | |||
+ | Thus, <math>bc=(-7)(-12)=84.</math> | ||
== See also == | == See also == |
Revision as of 02:16, 17 November 2007
Problem
Let be the graph of , and denote by the reflection of in the line . Let the equation of be written in the form
Find the product .
Solution
We need to find a formula for if .
With some algebra, we find this to be:
.
Substituting in, we get:
Expanding,
.
Thus,
See also
1988 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |