Trace the curve y2 = x2 (x + 1.n) by stating all the properties used to trace it
solution
by the help of polar coordinates
x = r cos
y = r sin
substituting
2 (r sin ) = 2 (r cos ) (r cos ) + n)
r sin = r cos (r cos + n)
r sin = r2 cos2 + n r cos
sin =r cos2 + n cos
r = sin / (cos 2 + n cos )
we can compute some values for r given
0 /4 /2
r 0 0.584 0
we know that the curve is asymmetrical since x =0 axis
attached a plot for n = 2
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