How do you convert $y = 2 x - 1$ $y=2x-1$ to polar form?

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Answer 1 · 2016-12-22T09:07:21

$r = \frac{1}{2 cos θ - sin θ}$ $r=1/(2costheta-sintheta)$

for polars

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

$x = r cos θ$ $x=rcostheta$

$y = r sin θ$ $y=rsintheta$

$y = 2 x - 1$ $y=2x-1$

$r sin θ = 2 r cos θ - 1$ $rsintheta=2rcostheta-1$

$\Rightarrow 2 r cos θ - r sin θ = 1$ $=>2rcostheta-rsintheta=1$

$r (2 cos θ - sin θ) = 1$ $r(2costheta-sintheta)=1$

$r = \frac{1}{2 cos θ - sin θ}$ $r=1/(2costheta-sintheta)$

How do you convert y=2x-1y=2x−1y=2x-1 to polar form?