<p>A hyperbola has the equation \(a(x-2)^2-b(y+1)^2=c\) where&nbsp;\(a\), \(b\), 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 \(c\).<span class="inline-marks">[4]</span></p>

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 \(c\).

Simultaneous Equations (3 Variables)

International Baccalaureate Higher Level Mathematics

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