Let \( f(x) = \frac{1}{4}x^2 + 2 \). The line \( L \) is the tangent to the curve of \( f \) at (4, 6).

Let \( g(x) = \frac{90}{3x + 4} \), for \( 2 \le x \le 12 \). The following diagram shows the graph of \( g \).

(a) Find the values of the constants for the equation of \( L \) [4]

(b) Find the values of the constants for the area of the region enclosed by the curve of \( g \), the \( x \)-axis, and the lines \( x = 2 \) and \( x = 12 \). Give your answer in the form \( a \ln b \), where \( a, b \in \mathbb{Z} \) [6]

(c) Find the values of the constants for the area enclosed by the lines \( L \), \( x = 2 \), \( x = 12 \), and the graph of \( h \), where the graph of \( g \) is reflected in the \( x \)-axis to give the graph of \( h \), and the area enclosed by \( L \), \( x = 2 \), \( x = 12 \), and the \( x \)-axis is 120 \( \text{cm}^2 \) [3]