A standard hyperbola x2a2−y2b2=1 of eccentricity 'e' is given as below.
Choose the correct options.[S is the focus and dotted line is a directrix.]
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AB=2a
QS=me
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 ≡ (a, 0); A ≡ (-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 QSQC=constant=e=QSm
∴ QS=em
S is the focus, given by the point (ae,o),and b≡(a,0)
∴ SB=ae−a
=a(e−1)