Difference between revisions of "1988 AIME Problems/Problem 14"

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== Problem ==
 
== Problem ==
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Let <math>C</math> be the [[graph]] of <math>xy = 1</math>, and denote by <math>C^*</math> the [[reflection]] of <math>C</math> in the line <math>y = 2x</math>.  Let the [[equation]] of <math>C^*</math> be written in the form
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<cmath>12x^2 + bxy + cy^2 + d = 0.</cmath>
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Find the product <math>bc</math>.
  
 
== Solution ==
 
== Solution ==
  
 
== See also ==
 
== See also ==
* [[1988 AIME Problems]]
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{{AIME box|year=1988|num-b=13|num-a=15}}
  
{{AIME box|year=1988|num-b=13|num-a=15}}
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[[Category:Intermediate Algebra Problems]]

Revision as of 19:37, 23 October 2007

Problem

Let $C$ be the graph of $xy = 1$, and denote by $C^*$ the reflection of $C$ in the line $y = 2x$. Let the equation of $C^*$ be written in the form

\[12x^2 + bxy + cy^2 + d = 0.\]

Find the product $bc$.

Solution

See also

1988 AIME (ProblemsAnswer KeyResources)
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
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