If the chord through the points whose eccentric angles are θ and ϕ on the ellipse x225+y29=1 passes through a focus, then the value of tan(θ/2) tan(ϕ/2) is

The equation of the line joining θ and ϕ isx5cos⁡θ+ϕ2+y3sin⁡θ+ϕ2=cos⁡θ−ϕ2If it passes through the point (4,0), then45cos⁡θ+ϕ2=cos⁡θ−ϕ2 or 45=cos⁡{(θ−ϕ)/2}cos⁡{(θ+ϕ)/2} or 4+54−5=cos⁡{(θ−ϕ)/2}+cos⁡{(θ+ϕ)/2}cos⁡{(θ−ϕ)/2}−cos⁡{(θ+ϕ)/2} =2cos⁡(θ/2)cos⁡(ϕ/2)2sin⁡(ϕ/2)sin⁡(θ/2)  or tan⁡θ2tan⁡ϕ2=−19If it passes through the point (-4,0), then tanϕ2tanθ2=9