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If the line a x+b y+c=0 is a normal to t...

If the line `a x+b y+c=0` is a normal to the curve `x y=1,` then `a >0,b >0` `a >0,b<0` `a<<0,b>>0` (d) `a<0,b<0` none of these

A

`a gt 0, b gt 0`

B

`a gt 0, b lt 0`

C

` a lt 0, b gt 0`

D

`a lt 0, b lt 0`

Text Solution

Verified by Experts

The correct Answer is:
B, C
Given, `" " xy = 1 rArr y = (1)/(x)`
`rArr " " (dy)/(dx) = - (1)/(x^(2))`
Thus, slope of normal = `x^(2)` ( which is always positive) and it is given `ax + by + c =0` is normal, whose slope `= -(a)/(b)`.
`rArr " " - (a)/(b) gt 0 or (a)/(b) lt 0`
Hence, a and b are of opposite sign.
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