A vertical line passing through the point $( h , 0 )$ intersects the ellipse $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 3 } = 1$ at the points $P$ and $Q$. Let the tangents to the ellipse at $P$ and $Q$ meet at the point $R$. If $\Delta ( h ) =$ area of the triangle $P Q R$, $\Delta _ { 1 } = \max _ { 1/2 \leq h \leq 1 } \Delta ( h )$ and $\Delta _ { 2 } = \min _ { 1/2 \leq h \leq 1 } \Delta ( h )$, then $\frac { 8 } { \sqrt { 5 } } \Delta _ { 1 } - 8 \Delta _ { 2 } =$