How do you write the equation using polar coordinates given $x^{2} = 4 y$ $x^2=4y$ ?

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Answer 1 · 2016-10-11T01:18:36

Substitute $r cos (θ)$ $rcos(theta)$ for x and $r sin (θ)$ $rsin(theta)$ for y.

Answer: $r = 4 \frac{sin (θ)}{{cos}^{2} (θ)}$ $r = 4sin(theta)/cos^2(theta)$

Substitute $r cos (θ)$ $rcos(theta)$ for x and $r sin (θ)$ $rsin(theta)$ for y:

${(r cos (θ))}^{2} = 4 (r sin (θ))$ $(rcos(theta))^2 = 4(rsin(theta))$

$r^{2} {cos}^{2} (θ) = 4 r sin (θ)$ $r^2cos^2(theta) = 4rsin(theta)$

Divide both sides by $r {cos}^{2} (θ)$ $rcos^2(theta)$ :

$r = 4 \frac{sin (θ)}{{cos}^{2} (θ)}$ $r = 4sin(theta)/cos^2(theta)$

How do you write the equation using polar coordinates given x^2=4yx2=4yx^2=4y?