If - - - - 3- then the chord joining the points - and - for the hyperbola x2a2 - y2b2 -1 passes through

The correct option is C one of the end points of the conugates axis #160;Equation of chord for hyperbola xacos (α βα) ybsin (α+βα)=cos (α+βα) xaco ...

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Byju's Answer

Standard XII

Mathematics

Focal Chord of Ellipse

If α + β = ...

Question

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

focus

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center

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one of the end points of the transverse axis

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one of the end points of the conugates axis

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Solution

The correct option is C one of the end points of the conugates axis
Equation of chord for hyperbola

$\frac{x}{a} cos (\frac{α - β}{α}) - \frac{y}{b} sin (\frac{α + β}{α}) = cos (\frac{α + β}{α})$

$\frac{x}{a} cos (\frac{α - β}{α}) + \frac{y}{b} = 0$

If $x = 0, y = b$

Thus, it passes through one of the endpoints of the conjugate axis.

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If α+β=3π then the chord joining the points α and β for the hyperbola x2a2−y2b2=1 passes through

The correct option is C one of the end points of the conugates axis Equation of chord for hyperbolaxacos(α−βα)−ybsin(α+βα)=cos(α+βα)xacos(α−βα)+yb=0If x=0,y=bThus, it passes through one of the endpoints of the conjugate axis.

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