The lines parallel to the normal to the ...

The lines parallel to the normal to the curve `x y=1` is/are (a)`3x+4y+5=0` (b) `3x-4y+5=0` (c)`4x+3y+5=0` (d) `3y-4x+5=0`

`3x+4y+5=0`

`3x-4y+5=0`

`4x+3y+5=0`

`3y-4x+5=0`

Text Solution

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The correct Answer is:

B, D

Differentiating xy = 1 w.r.t. x, we have
`(dy)/(dx)=-(1)/(x^(2))lt0`
Hence, the slope of normal at any point `P(x_(1),y_(1))` is
`x_(1)^(2)gt0`.
Therefore, the slope of normal must always be positive.
Hence, the possible lines are (2) and (4).

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