How do you find the rectangular equation for $r = \frac{1}{4 - cos θ}$ $r=1/(4-costheta)$ ?

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Answer 1 · 2016-09-28T19:28:02

$x^{2} + y^{2} = {(\frac{x + 1}{4})}^{2}$ $x^2+y^2=((x+1)/4)^2$ which is the equation of an ellipse.

${(x=rcos theta),(y=rsin theta):}$ so

$sqrt(x^2+y^2)=1/(4-x/sqrt(x^2+y^2))$ or

$sqrt(x^2+y^2)=sqrt(x^2+y^2)/(4 sqrt(x^2+y^2)-x)$ or

$4 sqrt(x^2+y^2)-x = 1$ or

$sqrt(x^2+y^2) = (x+1)/4$ Finally

$x^2+y^2=((x+1)/4)^2$ which is the equation of an ellipse.

How do you find the rectangular equation for r=1/(4-costheta)r=14−cosθr=1/(4-costheta)?