Q83 / 200 · AP EAMCET 2001 · Mathematics

The products of lengths of perpendiculars from any point of hyperbola $x^2-y^2=8$ to its asymptotes, is

A
$2$
B
$3$
Correct answer
C
$4$
D
$8$

Solution

We have the asymptotes are $x^2-y^2=0 \Rightarrow x= \pm y$ i.e. $x+y=0$ and $x-y=0$ The product of length of perpendiculars $=\left(\frac{x-y}{\sqrt{1^2+1^2}}\right)\left(\frac{x+y}{\sqrt{1^2+1^2}}\right)=\frac{x^2-y^2}{\sqrt{2} \cdot \sqrt{2}}=\frac{8}{2}=4$

Hence, the correct answer is option: 'C'.

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