If - and - are two points on the hyperbola x2-a2-y2-b2-1 and the chord joining these two points passes through the focus ae- 0 then e cos-2

The correct option is A Equation of the chord joining the points α and β on the hyperbola is x/a cos(α β/2) y/bsin(α+β/2)=cos(α+β/2) Since this line passes th ...

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Byju's Answer

Standard XII

Mathematics

Equation of Tangent in Point Form

If α and α ar...

Question

If $α$ and $α$ are two points on the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ and the chord joining these two points passes
through the focus (ae, 0) then e $c o s \frac{α - β}{2}$

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Solution

The correct option is A
Equation of the chord joining the points α and β on the hyperbola is
$\frac{x}{a} c o s (\frac{α - β}{2}) - \frac{y}{b} s i n (\frac{α + β}{2}) = c o s (\frac{α + β}{2})$
Since this line passes through the focus (ae, 0). We have e cos $(\frac{α - β}{2}) = c o s (\frac{α + β}{2})$

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Similar questions

Q. If

α + β = 3 π

then the chord joining the points

α

and

β

for the hyperbola

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

passes through

Q. 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} =

Q. If the chord joining the points

α

and

β

on the ellipse

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

subtends a right angle at (a, 0), then

tan (\frac{α}{2}) tan (\frac{β}{2}) =

What is the eccentricity of a hyperbola if a chord joining 2 points given by parameters $α$ and $β$ also passes through the focus. [Given : $α + β = p, α - β = q]$

Q. If

P (a s e c α, b t a n α)

and

Q (a s e c β, b t a n β)

are two points on the hyperbola

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

such that

α - β = 2 θ

(a costant), then PQ touches the hyperbola

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If α and α are two points on the hyperbola x2a2−y2b2=1 and the chord joining these two points passes through the focus (ae, 0) then e cosα−β2

The correct option is A Equation of the chord joining the points α and β on the hyperbola is xacos(α−β2)−ybsin(α+β2)=cos(α+β2) Since this line passes through the focus (ae, 0). We have e cos (α−β2)=cos(α+β2)

If $α$ and $α$ are two points on the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ and the chord joining these two points passes
through the focus (ae, 0) then e $c o s \frac{α - β}{2}$