<p>Find the number of ordered pairs <img alt="$(x,y)$" height="18" src="https://latex.artofproblemsolving.com/e/5/3/e53b1fe25be1c679117fb44a6a886fe1247d189a.png" width="40" />, where both <img alt="$x$" height="10" src="https://latex.artofproblemsolving.com/2/6/e/26eeb5258ca5099acf8fe96b2a1049c48c89a5e6.png" width="12" /> and <img alt="$y$" height="13" src="https://latex.artofproblemsolving.com/0/9/2/092e364e1d9d19ad5fffb0b46ef4cc7f2da02c1c.png" width="11" /> are integers between <img alt="$-100$" height="13" src="https://latex.artofproblemsolving.com/0/6/0/060d8850e65d5781ce12d9fe2681f401dd6ee77c.png" width="40" /> and <img alt="$100$" height="13" src="https://latex.artofproblemsolving.com/e/5/9/e59e2c6e83eb78cca610a5fd4070ae01c8d4ae60.png" width="26" /> inclusive, such that <img alt="$12x^2-xy-6y^2=0$" height="20" src="https://latex.artofproblemsolving.com/1/0/a/10a535646f69c9dc4230d60aca3118a2a563a884.png" width="162" />.</p>

Question No: 402

Find the number of ordered pairs $(x,y)$ , where both $x$ and $y$ are integers between $-100$ and $100$ inclusive, such that $12x^2-xy-6y^2=0$ .

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Tags: Algebra

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