The demand function $Q_1 = 80 − 4P_1$ intersects another demand function $Q_2$ at $P_1 = 5$. If the elasticity of the second demand function at that point is one-fourth of that of the first one, find $Q_2$ assuming it is a simple quadratic function.
$\underline{Attempt}$
Assuming $Q_2$ is a simple quadratic function defined $Q_2=aP_1^2+bP_1+c$
Since intersection point is $(5,60)$ we have
$25a+5b+c=60$
given that elasticity of the second demand function at that point is one-fourth of that of the first so we have
$$\frac{10a+b}{60/5}=\frac{1}{4}\times\frac{-4}{60/5}$$
I have only two equation so unable to find demand function $Q_2$. Can anyone help me to find demand function $Q_2$ ?