The equation of a line is y=e(^2x)-9 and the line has points at (0,a) and (b,0). Find the values of a and b.

y=e^2x-9. When x=0 y=a.a=e²⁽⁰⁾-9a=1-9=-8.
When x=b y=0.0=e^2(b)-99=e^2bln(9)=ln(e^2b)ln(9)=2b(1/2)ln(9)=bln(9^(1/2))=bb=ln3