Question

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


find the answer of this

Answer 1

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 $\Pi$ /4 $\Pi$ /2

r 0 0.584 0

we know that the curve is asymmetrical since x =0 axis

attached a plot for n = 2