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

Question

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

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

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Answer 1 · 2018-05-07T03:11:13

A

Explanation:

Converting from polar to rectangular:
$r^{2} = x^{2} + y^{2}$ $r^2= x^2+y^2$
$r cos θ = x$ $rcostheta=x$
$r sin θ = y$ $rsintheta=y$

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

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

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

Complete the square:

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

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

I would go with answer choice $A .$ $A.$

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

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

1 Answer

Explanation:

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Convert the polar equation to rectangular form? r=10 cos theta-6 sin thetar=10cosθ−6sinθr=10 cos theta-6 sin theta

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

1 Answer

Explanation:

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Impact of this question

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

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