If the chord through the points whose eccentric angles are - and - on the ellipse x2-a2- y2-b2 - 1 passes through the focus ae-0- then the value of tan -2 tan -2 -

If $(a s e c θ . b t a n θ)$ and $(a s e c Φ, b t a n Φ)$ are the ends of a focal chord of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ whose eccentricity is e,then $t a n \frac{θ}{2} \times t a n \frac{⊘}{2}$ equal to.

Q. Let an ellipse

E : \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1,

a^{2} > b^{2},

passes through

(\sqrt{\frac{3}{2}}, 1)

, and has eccentricity

\frac{1}{\sqrt{3}}

. If a circle, centered at focus

F (α, 0),

(α > 0),

E

and radius

\frac{2}{\sqrt{3}}

, intersects

E

at two points

P

and

Q,

then

P Q^{2}

is equal to

Q. If normal to the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

(a e, \frac{b^{2}}{a})

is passing through

(0, - 2 b)

, then

e =

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If the chord through the points whose eccentric angles are α and β on the ellipse x2a2+y2b2=1 passes through the focus (ae,0), then the value of tan α2 tan β2=

If the chord through the points whose eccentric angles are $α$ and $β$ on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ passes through the focus $(a e, 0),$ then the value of tan $\frac{α}{2}$ tan $\frac{β}{2} =$