Did You Know what Actually is Point of Inflection ? ( Part-2 )

Let $I$ be the point of inflexion which is given by $y''=0$ and solving this we get inflexion point as $I(1,b-a-2)$ . Using one point form and slope through first derivative at this point, first tangent can be written as $y=(-a-3)x+b+1$ . Using two point form between $I$ and $P$ we can also get different form of same slope. So equating the slope we get $\large -ah-3=\frac{b-a-2-2+5h}{1-h}$ Comparing coefficients of $h$ we get $\boxed{a=2,b=1}$