How do you convert $r {sin}^{2} θ = 3 cos θ$ $r \sin^2 \theta =3 \cos \theta$ into rectangular form?

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Answer 1 · 2018-04-11T08:17:00

The rectangular form is $y^{2} = 3 x$ $y^2=3x$

To convert from polar coordinates to rectangular coordinates, apply the following

$sin θ = \frac{y}{r}$ $sintheta=y/r$

$cos θ = \frac{x}{r}$ $costheta=x/r$

$tan θ = \frac{y}{x}$ $tantheta=y/x$

and

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

Therefore,

$r {sin}^{2} θ = 3 cos θ$ $rsin^2theta=3costheta$

$\Leftrightarrow$ $<=>$ , $r \cdot \frac{y^{2}}{r^{2}} = 3 \frac{x}{r}$ $r*y^2/r^2=3x/r$

$\Leftrightarrow$ $<=>$ , $y^{2} = 3 x$ $y^2=3x$

This is the equation of a parabola.

graph{(y^2-3x)=0 [-3.375, 16.625, -4.36, 5.64]}

How do you convert r \sin^2 \theta =3 \cos \thetarsin2θ=3cosθr \sin^2 \theta =3 \cos \theta into rectangular form?