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.#