Question

Question #e5d5b

Answer 1

Should this be `b^2-bx-20x^2=?`
If this is so then you will have an infinite range of value satisfying the equation.

Explanation:

As on our 1 to 1 discussion:

Factorising gives:`(b+4x)(b-5x)`

Your equation is the `ul("equivalent")` of:

`z=y^2-xy-20x^2 larr" saddle"`

This is a 3-dimemsional equation (3 space)

Set `z=0=(y+4x)(y-5x)`

`=> y=-4x"; "y=+5x`

are solutions to `z=0`

That is: the intersection of the saddle and plane are all the solutions for `z=0`.

As they two have different gradients it indicates the axis of the saddle are not parallel to the xy plane axis.
I suspect the saddles equivalent to the y-axis will be parallel half way between `y=-4x" and "y=5x`

If you plot using the information from the factorization where `z=0` we obtain a different plot for:
`z=0=y^2-xy-20x^2 -> y=(20x^2)/(y-x)`