Convert the polar equation to rectangular form? $r=10 cos theta-6 sin theta$

Question

A. $(x-5)^2 + (y+3)^2 =34$
B. $(x-3)^2 + (y-5)^2 =34$
C. y=10 sinx - 6 cos x
D. r=10x-6y

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Answer 1 · 2018-05-07T03:11:13

A

Converting from polar to rectangular:
$r^2= x^2+y^2$
$rcostheta=x$
$rsintheta=y$

$r=10 cos theta-6 sin theta$
Multiply by $r$ on both sides:
$r^2= 10rcostheta-6rsintheta$

$x^2+y^2= 10x-6y$

$x^2-10x+y^2+6y=0$

Complete the square:

$x^2-10x+25+y^2+6y+9=34$

$(x-5)^2+(y+3)^2= 34$

I would go with answer choice $A.$