Consider a steady one dimensional heat flow in a plate of $25$ mm thickness with a uniform heat generation of $100M\frac{W}{m^2}$ follows the relation $T(x)=(-\frac{q}{2}K)x^2+C_{1}x+C_2.$ The left and right faces are kept at the constant temperature of $160C$ and $120C$ respectively Take, $K_{\text{p}\text{l}\text{a}\text{t}\text{e}}=200\frac{W}{m}K.$ Calculate the following:

$($a$)$ The maximum temperature within the plate in $0$ C $.$

$($b$)$ The location of maximum temperature within the plate from its right end.