Find the points on the curve `x y+4=0` at which the tangents are inclined at an angle of `45^0` with the `x-`a xi s .

Explanation

given curve is `x y+4=0`
we have to go looking out the points on the curve at that the tangents square measure inclined at an angle of `45^0`
with the `x-`a xi s.
differentiate the equation w.r.t` x `we get
`(dy)/(dx)=4/x^2`
We've the slope of the tangent at (x,y) is `(dy)/(dx)`
According to the question `(dy)/(dx)=tan(45^0)`
so,`=>4/x^2=1`
`=>x^2=4`
`=>x=pm2`
If `x=2` then `y=-2` and if `x=-2` then `y=2`
points are `(2,-2) or (-2,2)`