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'Cocked Hat' printed from http://nrich.maths.org/
The implicit equation
$$(x^2 + 2a y -a^2)^2 = y^2(a^2 - x^2)$$
represents a family of functions the members of the family
corresponding to different values of $a$.
Re-arrange the equation into the form $y= f(x)$ and draw some
graphs belonging to the family for different values of $a$. What is
the domain of the function $f(x)$?
For investigating these graphs you can download the shareware
program Graphmatica for free from here
NRICH is an approved distributor of this program. You can find more
information about the program from http://www.graphmatica.com/