If ax2 + bx + c = a(x - p)2, then the relation among a, b, c would be?

Answer: Option C

$$\begin{array}{rl}& a{x}^2+bx+c=a{\left(x-p\right)}^2\\ & \Rightarrow a{x}^2+bx+c=a{\left(x^2+p^2-2px\right)}^2\\ & \Rightarrow a{x}^2+bx+c=a{x}^2+a{p}^2-2apx\\ & \text{Comparing confficients of }{x}^2\text{and }x\\ & \Rightarrow b=-2ap\\ & \Rightarrow p=-\frac{b}{2a}.......(1)\\ & andc=a{p}^2\\ & \Rightarrow c=a\times \frac{b^2}{4a^2}\left[\text{From (i)}\right]\\ & \Rightarrow 4ac=b^2\end{array}$$