i have problem in (c)

$\displaystyle (4m^2+1)x^2 +8m (1-2m)x+4(4m^2-4m -3)=0 $

then i have to solve the parametric equations:

(x-coordinate of M )$\displaystyle x= -\frac{4m(1-2m)}{4m^2+1}$

and $\displaystyle y-1 = m(x-2)$

is there any other method beside put $\displaystyle m = \frac {y-1}{x-2}$ back to $\displaystyle x= -\frac{4m(1-2m)}{4m^2+1}$ ?

here's the question:

thanks!