A line cuts a circle

7 written marks

The line \(2x+y=5\) meets the circle \(x^2+y^2=10\) at \(A\) and \(B\).

1. Eliminate \(y\) to obtain a quadratic equation for \(x\).

   [2]

2. Find the coordinates of \(A\) and \(B\).

   [3]

3. Find the exact length \(AB\).

   [2]

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