Touch 'n Go

Geometry Level 3

The line \(y=mx+10\) is tangent to the curve \(\large \dfrac{x-y+7}{7-y}+\dfrac{5x+7}{5x+8}=2\) at the points \((x_1,y_1)\) and \((x_2,y_2)\).

If \(x_1 \times y_2+x_2 \times y_1\) can be written as \(\large \frac{a}{b}\) for coprime positive integers \(a\) and \(b,\) find \(a+b\).

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