# Question e5d5b

Feb 14, 2017

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:$\left(b + 4 x\right) \left(b - 5 x\right)$

Your equation is the $\underline{\text{equivalent}}$ of:

$z = {y}^{2} - x y - 20 {x}^{2} \leftarrow \text{ saddle}$

This is a 3-dimemsional equation (3 space)

Set $z = 0 = \left(y + 4 x\right) \left(y - 5 x\right)$

$\implies y = - 4 x \text{; } y = + 5 x$

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 $y = - 4 x \text{ and } y = 5 x$

If you plot using the information from the factorization where $z = 0$ we obtain a different plot for:
$z = 0 = {y}^{2} - x y - 20 {x}^{2} \to y = \frac{20 {x}^{2}}{y - x}$