Question #e5d5b

1 Answer
Tony B
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:# (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)

Tony B

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)#

Tony B

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