Question

If chord joining the points P(a) and Q (B) on the ellipse (x2 /64) + (y/16) = 1 subtends a right angle at the vertex A (8,0), then the value of the tan (a/2) tan (B/2) is​

Answer 1

Step-by-step explanation:

Correct option is

A

b

2

−a

2

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

(b

2

+a

2

)Cos(α−β)=(b

2

−a

2

)Cos(α+β)

b

2

−a

2

b

2

+a

2

=

Cos(α−β)

Cos(α+β)

a

2

b

2

=

Cos(α+β)−Cos(α−β)

Cos(α+β)+Cos(α−β)

Finally , We get

tanαtanβ=

b

2

−a

2