The equation expressing a novel type of egg shaped curve
(obtained by the method using the difference between the first and the second order equations)
proposed by Mr. Yasuyuki ASAI is written in the following;
,
(1)
or, is written in the expression of factorization as
.
(2)
In this time, we treat Eq.(2). The solution of Eq.(2) is given as
.
(3)
Four points with which the curves displayed by Eq.(3) intersect the x axis
are obtained by the following equation into which Eq.(3) is put as y=0.
.
(4)
If we solve the above equation, we obtain as
,
(5)
,
(6)
and
.
(7)
In the recommended case that ,
Eq.(3) gives an egg shaped curve in the region of
and another accompanied curve in the region of .
In the other regions, any curves do not exist.
These are shown in Fig.1.
