Question

find an equation equivalent to r= 1+2 = sin theta in rectangular coordinates

Answer 1

Answer:

C

Step-by-step explanation:

$x^{2}$+$y^{2}$= $\sqrt{x^{2}+y^{2} }$+2y

Answer 2

Answer:

The equation of equivalent is,$x^{4}+ y^{4} +3 y^{2} +2x^{2} y^{2} -4y^{3} -4 x^{2} y-x^{2} =0$

Step-by-step explanation:

Definition of equivalent equation:

If two systems of equations have the same solution, they are equivalent (s). This article explains how to determine whether two systems are equal. Equivalent systems are sets of equations that have the same solution.

Given, r = 1+2sinФ

$r^{2} =r+2rsin$θ

$x^{2}+ y^{2} =r+2y\\x^{2} + y^{2} -2y=r$

Squaring, both side:

$(x^{4} +y^{4} -2 y^{2}) = r^{2} \\x^{4}+ y^{4} + 4y^{2}+2 x^{2} y^{2} - 4y^{3} -4x^{2} y =x^{2} +y^{2} \\x^{4} + y^{4} +3 y^{2} +2 x^{2} y^{2} -4y^{3} -4x^{2} y^}-x^{2} =0$

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