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- The diagram shows the line \(2 y = x + 5\) and the curve \(y = x ^ { 2 } - 4 x + 7\), which intersect at the points \(A\) and \(B\). Find
(a) the \(x\)-coordinates of \(A\) and \(B\),
(b) the equation of the tangent to the curve at \(B\),
(c) the acute angle, in degrees correct to 1 decimal place, between this tangent and the line \(2 y = x + 5\). - Determine the set of values of \(k\) for which the line \(2 y = x + k\) does not intersect the curve \(y = x ^ { 2 } - 4 x + 7\).
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}