# A special type of function...

• December 17th 2006, 08:12 PM
anak
A special type of function...
x^4 - (5x^2)(y^2) + 4y^4 = 0

What do you call this type of function and how do you graph it? I can't seem to find any way on my '84
• December 18th 2006, 04:06 AM
Soroban
Hello, anak!

Quote:

$x^4 - 5x^2y^2 + 4y^4 \:= \:0$

What do you call this type of function and how do you graph it?

I'm not familiar with any name for this type.
It is a quartic function, but it is "degenerate".

It factors: . $(x^2 - y^2)(x^2 - 4y^2) \:=\:0$

Hence, we have: . $\begin{array}{cc}x^2-y^2\:=\:0 \;\; \Rightarrow\;\; y^2 = x^2\;\;\Rightarrow\;\; y = \pm x \\ x^2-4y^2\:=\:0 \;\;\Rightarrow\;\; y^2 = \frac{x^2}{4} \;\;\Rightarrow\;\; y = \pm\frac{1}{2}x\end{array}$

The graph is two pairs of lines intersecting at the origin.