Fun with Ellipse

On the ellipse $\frac { { x }^{ 2 } }{ 64 } +\frac { { y }^{ 2 } }{ 9 } =1$ , tangents drawn at ${ P }_{ 1 },{ P }_{ 2 },{ P }_{ 3 },...{ P }_{ n }$ intersect the major axis at ${ T }_{ 1 },{ T }_{ 2 },{ T }_{ 3 },...{ T }_{ n }$ respectively,

if the value of $\sum _{ i=1 }^{ n }{ \frac { { { Area }\left( { \Delta }{ P }_{ i }{ T }_{ i }{ S } \right) }*{ Area }\left( { \Delta }{ P }_{ i }{ T }_{ i }{ S }' \right) }{ { \left( P_{ i }{ T }_{ i } \right) }^{ 2 } } } = 18$ , then $n$ equal to?

where $S$ and $S'$ represents the two focus of ellipse.