Answer to Question #133304 in Calculus for rahul singh

Question #133304
Trace the curve y 2 =x2(x+ 1. n ) by stating all the
properties used to trace it.


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Expert's answer
2020-09-21T12:29:33-0400

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 \empty

y = r sin \emptyset

substituting

2 (r sin \empty ) = 2 (r cos \empty ) (r cos \empty ) + n)

r sin \empty = r cos \empty (r cos \empty + n)

r sin \empty = r2 cos2 \empty + n r cos \empty

sin \empty =r cos2 \empty + n cos \empty

r = sin \empty / (cos 2 \empty + n cos \empty )

we can compute some values for r given \empty

\empty 0 Π\Pi /4 Π\Pi /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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