If a, b are the eccentric angles of the
extremities of a focal chord of the ellipse
x2/16+y2/9=1 then tan(α/2)tan(β/2)=
7+47−4
−923
5−45+4
87−239
The eccentricity e=1−916=74
Let P(4cosα,3sinα) and Q(4cosβ,3sinβ)
be a focal chord of the ellipse passing
through the focus at (7,0)
Then 3sinβ4cosβ−7=3sinα4cosα−7
⇒ sin(α−β)sinα−sinβ=74⇒ cos[(α−β)/2]cos[(α+β)/2]=74⇒ tanα2tanβ2=7−47+4=23−87−9