How do you write $- 2 x + 4 y = 9$ $-2x+4y=9$ in polar form?

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Answer 1 · 2016-11-25T10:51:34

The polar equation is $r = \frac{9}{4 sin θ - 2 cos θ}$ $r=9/(4sin theta-2costheta)$

To transform from rectangular coordinates $(x, y)$ $(x,y)$ to polar coordinates $(r, θ)$ $(r,theta)$ , we use the following equations

$x = r cos θ$ $x=rcostheta$

$y = r sin θ$ $y=rsintheta$

Therefore,

we can rewrite, $- 2 x + 4 y = 9$ $-2x+4y=9$

as $- 2 r cos θ + 4 r sin θ = 9$ $-2rcostheta+4rsintheta=9$

$r (4 sin θ - 2 cos θ) = 9$ $r(4sin theta-2costheta)=9$

$r = \frac{9}{4 sin θ - 2 cos θ}$ $r=9/(4sin theta-2costheta)$

How do you write -2x+4y=9−2x+4y=9-2x+4y=9 in polar form?