c=√(9+ 16)=5

Equation of a straight line passing through the right focus (5,0) and parallel to the asymptote: y=4/3(x-5)

x^2/9-y^2/ 16= 1

16x^2-9y^2= 144

16x^2-9[4/3(x-5)]^2= 144

16x^2- 16x^2+ 160x-400= 144

160x=544

x= 17/5

y=4/3( 17/5-5)

=-32/ 15

P( 17/5，-32/ 15)

A(-3，0) A'(3，0)

sδPAA ' = 1/2 | 3-(-3)| * |-32/ 15 |

=32/5