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.Find the product of lengths of the perp...

.Find the product of lengths of the perpendiculars from any point on the hyperbola `x^2/16-y^2/9=1` to its asymptotes.

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a=4, b=3 equation of asymptotes are=`y=pm(b/a)x` Required Equations:- `3x+4y=0` & `3x-4y=0`
Lets points on hyperbola be `A(4,0) & B(-4,0)` `d1=|(3*4+4*0)/5|=12/5`
`d2=|(3*4-4*0)/5|= 12/5` `product =d1*d2= 144/25=5.76`
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