Mathematics

Problem

For a parabola

y^{2} = 4ax

, let

\Delta_{1}

be the area of the triangle formed by three points

P

Q

, and

R

on the curve. Let

\Delta_{2}

be the area of the triangle formed by the tangents drawn to the parabola at these three points. If

\Delta_{1}

is calculated to be

64

square units, determine the value of

\Delta_{2}