Definition of impact parameter David Morin defines impact parameter as:

which is the semi minor axis of the conic.
But according to Wikipedia and some other sources:

It is the perpendicular distance from the center of potential to an asymptote to the trajectory...which is the perpendicular joining the focus to the asymptote.
Which is the correct definition? Are they equivalent?
 A: To show that the impact parameter is equal to the semi minor axis of a hyperbola
$a$ = semi-major axis of hyperbola
$b$ = semi-minor axis of hyperbola
D and D' are the directrices.
V and V' are the vertices.
 $\varepsilon$ = $\sqrt{1 + (b/a)^{2}}$ (for hyperbola)
$\varepsilon$ = eccentricity of conic
$OV = OV' = a$
$VV' = 2a$
$FV = \varepsilon VD'$
$FV' = \varepsilon V'D'$
$FV+FV' = \varepsilon(VD'+V'D')$
$\Rightarrow OF-OV+OF+OV' = 2a\varepsilon$
$\Rightarrow OF = OF' = a\varepsilon$
The equation of one of the asymptotes is:
$y = -(b/a)x$...(1)
Let the equation of the perpendicular to the asymptote be:
$y = (a/b) x + c $...(2), where c is a constant
As the perpendicular passes through $(-a\varepsilon , 0)$, putting the values in the above equation we get:
$c = a^{2} \varepsilon/b$
The equation of the perpendicular becomes:
$y = (a/b) x + (a^{2} \varepsilon/b) $ ...(3)
We can find the intersection point of the asymptote and its perpendicular by solving equations (1) and (3)
Solving the equations we get:
$x = -a^{2}/(\sqrt{a^{2} + b^{2}})  
\Rightarrow x = -a/\varepsilon$
$y = ab/\sqrt{a^{2} + b^{2}}$
$\Rightarrow y = b/\varepsilon$
The distance between the focus $(-a\varepsilon , 0)$ and the intersection of the asymptote and its perpendicular $(-a/\varepsilon , b/\varepsilon)$ is:
$(say)b' = \sqrt{(a\varepsilon - a/\varepsilon)^{2} + (b/\varepsilon)^{2}}$
$\Rightarrow b' =  \sqrt{a^{2} \varepsilon^{2} -2a^{2}+((a^{2}+b^{2})/\varepsilon ^{2})}$
$\Rightarrow b' = \sqrt{a^{2}\varepsilon ^{2} - 2a^{2} + a^{2}}$
$\Rightarrow b' =  a\sqrt{\varepsilon ^{2} - 1}$
$\Rightarrow b' =  b$
Therefore, the perpendicular distance between the focus and the point intersection of the asymptote and its perpendicular is equal to the semi minor axis.
So the claim that the Impact parameter and the semi minor axis are equal is true.

P.S.I figured out the solution so I posted it. If u guys got better/faster methods plz give ur solution.
