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

Options

A. `a gt 0, b gt 0`
B. `a gt 0, b lt 0`
C. `a lt 0, b lt 0`
D. Data is insufficient

Answer

B

Explanation

The given equation of curve is `xy=1`
`impliesx (dy)/(dx)=-yimplies(dy)/(dx)=-y/x`
Let `(t,1/t)` be any point on the curve at which normal to the curve can be drawn.
`:.((dy)/(dx))_((t,1/t))=-1/(t^(2))`
So slope of normal `=t^(2)`
Line `ax+by+c=0` will be normal to the curve if
`t^(2)=(-a)/bimpliest^(2)gt0`
`implies(-a)/bgt0,` if `bgt0, a lt0,` or `b lt0, a gt0`