Let P be a variable point on the parabola \(y^2 = 2x\), and Let B and C be points on the y-axis so that the circle \((x - 1)^2 + y^2 = 1\) is inscribed in triangle PBC. Find the minimum area of triangle PBC.
Quadratic formula: root of ax^2 + bx + c = 0 is x = (-b pm sqrt(b^2 - 4ac))/2a
Minimum area of triangle PBC is 12.
