Problem

(a) Express $4x^2+10x+6$ in the form $a(x+b)^2+c$, where $a$, $b$ and $c$ are rational constants to be determined.

(b) The curve with equation $y=4x^2+10x+6$ and the line $y=k$ have exactly one point of intersection.

Using your answer to part (a) or otherwise, state the value of the constant $k$.