MCQ
If $ PN$ is the perpendicular from a point on a rectangular hyperbola $x^2 - y^2 = a^2 $ on any of its asymptotes, then the locus of the mid point of $PN$ is :
- Aa circle
- Ba parabola
- Can ellipse
- ✓a hyperbola
$\Rightarrow 2h = ct\ \&\ 2\ = 2c/t $
$\Rightarrow xy = c^2/2$
alternatively
$P $ $: (a sec \theta , a tan \theta ) ; $
$N : [(a/2) (sec \theta + tan \theta ) , (a/2) (sec \theta + tan \theta )]$
$\Rightarrow$ $ 4h/a = 2 sec \theta + tan \theta \,\,\& \,\,4k/a = sec \theta + 2 tan \theta $
$\Rightarrow x^2 - y^2 = 3a^2/16 $
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