Question

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

• A. cos
• B.
• C.
• D. cos

Answer 1

The correct option is B

we should do good if we know the chords equation joining 2 points of a hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

which is,

$\frac{x}{a}.cos\left[\frac{\alpha -\beta }{2}\right]-\frac{y}{b}.sin.\left[\frac{\alpha +\beta }{2}\right]=cos\left[\frac{\alpha +\beta }{2}\right]$

since this process through focus (ae,0)

$e.cos\left[\frac{\alpha -\beta }{2}\right]-0=cos\left[\frac{\alpha +\beta }{2}\right]$

$\therefore e=\frac{cos\left[\frac{\alpha +\beta }{2}\right]}{cos\left[\frac{\alpha -\beta }{2}\right]}=\frac{cos\frac{p}{2}}{cos\frac{q}{2}}$

Hence option (b)