If the line `ax+by+c=0` is a tangent to the curve `xy=4` then

Options

A. `alt0,bgt0`
B. `ale0,bgt0`
C. `alt0,blt0`
D. `ale0,blt0`

Answer

C

Explanation

Given `xy=4`
`impliesy=4/x`
`:.(dy)/(dx)=-4/(x^(2))`…………i
Given equation of line is `ax+by+c=0`
`impliesy=(-a)/b x=c/b`
Slope of a line `=(-a)/b`………..ii
From Eq. i and ii we get
`-4/(x^(2))=-a/bimpliesx^(2)=(4b)/a gt0`
which is true,when
`agt0, bgt0` or `alt0, blt0`