The correct option is A −a2b2
To find value of tanαtanβ
Parametric form of Points are
P(acosα,bsinα), Q(−asinβ,bcosβ)
Since OP and OQ are Perpendicular
OP.OQ = 0
acosα[−asinβ]+bsinα[bcosβ]=0
On Simplifying this , we get
(b2+a2)Cos(α−β)=(b2−a2)Cos(α+β)
b2+a2b2−a2=Cos(α+β)Cos(α−β)
b2a2=Cos(α+β)+Cos(α−β)Cos(α+β)−Cos(α−β)
Finally , We get
tanαtanβ=−a2b2
Hence , Option A