A hyperbola has the equation $a(x-2)^2-b(y+1)^2=c$ where $a$, $b$, and $c$ are positive

Question

A hyperbola has the equation $a(x-2)^2-b(y+1)^2=c$ where $a$, $b$, and $c$ are positive integers. It passes through the point $(7,10)$. A line $y=x-1$ intersects the hyperbola at $x=1$. Find one possible value for each of $a$, $b$ and $c$.[4]

Accepted Answer

One possible choice is $a=5,b=1,c=4$.

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Solution:

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