Answer:
Step-by-step explanation:
r = 1+2sinФ
multiplying both sides by r ,we get
[tex]r^2= r+2rsin[/tex]Ф
[tex]x^2+y^2= r + 2y[/tex] [ since rsinФ = y ]
[tex]x^2+y^2-2y= r[/tex]
[tex](x^2+y^2-2y)^2 = r^2\\x^4+y^4+4y^2+2x^2y^2-4y^3-4x^2y=x^2+y^2\\x^4+y^4+3y^2+2x^2y^2-4y^3-4x^2y-x^2 =0[/tex]
The equation equivalent to r = 1 + 2 is mathematically given as
(x^2+y^2-2y)^{2}=x^2+y^2
Question Parameter(s):
r = 1 + 2
Generally, the equation for the polar cordinates is mathematically given as
[tex]x=rsin\theta\\\\y=rcos\theta[/tex]
Therefore
[tex](sin^{2}\theta + cos^{2}\theta) = 1[/tex]
Hence
[tex]r=\sqrt{x^2+y^2}[/tex]
In conclusion
[tex]\sqrt{x^2+y^2} = 1+2\frac{y}{\sqrt{x^2+y^2}}\\\\x^2+y^2-2y= \sqrt{x^2+y^2}[/tex]
(x^2+y^2-2y)^{2}=x^2+y^2
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