Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 6"
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| − | + | Let <math>P_{1}: y=x^{2}+\frac{101}{100}</math> and <math>P_{2}: x=y^{2}+\frac{45}{4}</math> be two parabolas in the cartesian plane. Let <math>\mathcal{L}</math> be the common tangent of <math>P_{1}</math> and <math>P_{2}</math> that has a rational slope. If <math>\mathcal{L}</math> is written in the form <math>ax+by=c</math> for positive integers <math>a,b,c</math> where <math>\gcd(a,b,c)=1</math>. Find <math>a+b+c</math>. | |
| − | [[Mock AIME 1 2006-2007]] | + | ==Solution== |
| + | {{solution}} | ||
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| + | ---- | ||
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| + | *[[Mock AIME 1 2006-2007/Problem 5 | Previous Problem]] | ||
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| + | *[[Mock AIME 1 2006-2007/Problem 7 | Next Problem]] | ||
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| + | *[[Mock AIME 1 2006-2007]] | ||
Revision as of 16:27, 17 August 2006
Let 
and 
be two parabolas in the cartesian plane. Let 
be the common tangent of 
and 
that has a rational slope. If is written in the form 
for positive integers 
where 
. Find 
.
Solution
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