Question

A standard hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ of eccentricity 'e' is given as below.

Choose the correct options.[S is the focus and dotted line is a directrix.]

• A. \)
• B. AB=2a
• C. QS=me
• D. SB=a(e-1)

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A

\)

B

AB=2a

C

QS=me

D

SB=a(e-1)

This question basically maps the basic parameters of a hyperbola to its graphical form. It also gives an insight into the construction of the

hyperbola as well.

The vertex of the hyperbola are given by the points B $\equiv$ (a, 0); A $\equiv$ (-a, 0)

CD represents the conjugate axis of the hyperbola.

As you know hyperbola is the locus of points line is a constant, greater than one.

So if Q(m,b) is a points on the hyperbola $\frac{QS}{QC}=constant=e=\frac{QS}{m}$

$\therefore QS=em$

S is the focus, given by the point (ae,o),and b$\equiv$(a,0)

$\therefore SB=ae-a$

$=a(e-1)$