If a- -btan - and a- -b tan- are the ends of a focal chord of x2a2-y2b2-1- then tan-2-tan-2 equals to

The correct option is B 1 e1+e ...

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Standard XII

Mathematics

Directrix of Hyperbola

If aθ ,btan...

Question

If $(a sec θ, b tan θ)$ and $(a sec ϕ, b tan ϕ)$ are the ends of a focal chord of $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1,$ then $tan \frac{θ}{2} . tan \frac{ϕ}{2}$ equals to

\frac{e - 1}{e + 1}

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\frac{1 - e}{1 + e}

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\frac{1 + e}{1 - e}

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\frac{e + 1}{e - 1}

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Solution

The correct option is B $\frac{1 - e}{1 + e}$

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Similar questions

Q. If

(a sec θ, b tan θ)

and

(a sec ϕ, b tan ϕ)

are the ends of a focal chord of

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

, the value of

tan \frac{θ}{2} \cdot tan \frac{ϕ}{2}

can be equal to :

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. If

(a sec θ, b tan θ)

and

(a sec ϕ, b tan ϕ)

be the coordinates of the ends of a focal chord of the hyperbola

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

, then

tan \frac{θ}{2} tan \frac{ϕ}{2} =

Q. If

cos θ = \frac{cos α - e}{1 - e cos α}

, then find:

(tan \frac{θ}{2} + \sqrt{\frac{1 + e}{1 - e}} tan \frac{α}{2}) (tan \frac{θ}{2} - \sqrt{\frac{1 + e}{1 - e}} tan \frac{α}{2})

Q. If e and e’ are the eccentricities of the hyperbola

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

and its conjugate hyperbola the value of

\frac{1}{e^{2}} + \frac{1}{e^{‘ 2}}

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If (asecθ,btanθ) and (asecϕ,btanϕ) are the ends of a focal chord of x2a2−y2b2=1, then tanθ2.tanϕ2 equals to

The correct option is B 1−e1+e

If $(a sec θ, b tan θ)$ and $(a sec ϕ, b tan ϕ)$ are the ends of a focal chord of $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1,$ then $tan \frac{θ}{2} . tan \frac{ϕ}{2}$ equals to

The correct option is B $\frac{1 - e}{1 + e}$