The foot of the perpendicular from the focus to an asymptote of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}}$ = 1 is

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Solution

The correct option is B
Focus of S=(ae,0) Equation of one asymptote is bx-ay=0
Let (h,k) be the foot of the perpendicular from S to bx-ay=0
Then $\frac{h - a e}{b} = \frac{k - 0}{- a} = \frac{- a b e}{a^{2} + b^{2}} \Rightarrow \frac{h - a e}{b} = \frac{- a b e}{a^{2} e^{2}} & \frac{k}{- a} = \frac{- a b e}{a^{2} e^{2}}$
On simplification, we get h= $\frac{a}{e}, k = \frac{b}{e}$
Foot of the perpendicular is $(\frac{a}{e}, \frac{b}{e})$

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