2018 UNCO Math Contest II Problems/Problem 3
Find all values of that have the property that if lies on the hyperbola , then so does the point .
We can write a system of equations -
Expanding the second equation, we get .
Since we want this to look like , we plug in B's that would put it into that form. If we plug in , things cancel, and we get . So ~Ultraman
Solution 2 (Grinding)
As with Solution 1, we create a system of equations.
Through expanding the second equation, we get . Since , we have The terms on each side cancel out, so the equation becomes The coefficient of on the RHS is and the coefficient of is . From these two observations, we now create two new equations. Solving either equation and then checking with the other will reveal that . ~kingme271
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