Given a vector function $E=y{a}_x+x{a}_y,$ evaluate the line integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}E*dl$ from P$1(2,1,-1)$ to P$2(8,2,-1)$

a$)$ along the parabola $x=2y^2$

b$)$ along the straight line joining the two points

Is this $E$ a conservative field?