How do you convert $r = 5 cos θ$ $r=5costheta$ into rectangular equations?

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Answer 1 · 2017-01-20T08:20:39

$x^{2} + y^{2} - 5 x = 0$ $x^2+y^2-5x=0$

I take it that this means converting to Cartesian form. For conversion of Polar to and from Cartesian we use the eqns.

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

$x = r cos θ$ $x=rcostheta$
$y = r sin θ$ $y=rsintheta$

for
$r = 5 cos θ$ $r=5costheta$

multiply both sides by $r$ $r$

$r^{2} = 5 r cos θ$ $r^2=5rcostheta$

using the above conversion eqns.

$x^{2} + y^{2} = 5 x$ $x^2+y^2=5x$

$x^{2} + y^{2} - 5 x = 0$ $x^2+y^2-5x=0$

How do you convert r=5costhetar=5cosθr=5costheta into rectangular equations?