Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 6"

 
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6. 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>.
 
6. 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>.
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[[Mock AIME 1 2006-2007]]

Revision as of 15:57, 24 July 2006

6. Let $P_{1}: y=x^{2}+\frac{101}{100}$ and $P_{2}: x=y^{2}+\frac{45}{4}$ be two parabolas in the cartesian plane. Let $\mathcal{L}$ be the common tangent of $P_{1}$ and $P_{2}$ that has a rational slope. If $\mathcal{L}$ is written in the form $ax+by=c$ for positive integers $a,b,c$ where $\gcd(a,b,c)=1$. Find $a+b+c$.

Mock AIME 1 2006-2007