How do you convert $2 x - 3 y = 5$ $2x-3y=5$ into polar form?

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How do you convert $2 x - 3 y = 5$ $2x-3y=5$ into polar form?

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Answer 1 · 2016-02-29T12:21:47

$r = \frac{5}{2 cos θ - 3 sin θ}$ $r = 5/(2costheta - 3sintheta )$

Explanation:

Using the formulae that links Cartesian to Polar coordinates.

$∙ x = r cos θ$ $• x = rcostheta$

$∙ y = r sin θ$ $• y = rsintheta$

hence 2x - 3y = 5 , becomes :

$2 r cos θ - 3 r sin θ = 5$ $2rcostheta - 3rsintheta = 5$

take out common factor of r

$r (2 cos θ - 3 sin θ) = 5$ $r(2costheta - 3sintheta ) = 5$

$\Rightarrow r = \frac{5}{2 cos θ - 3 sin θ}$ $rArr r = 5/(2costheta - 3sintheta )$

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How do you convert $2 x - 3 y = 5$ $2x-3y=5$ into polar form?

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