How do you convert #r = 10/(4 - 7cos(theta))# to rectangular form?

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Answer 1 · 2016-05-06T18:04:35

#33x^2 -16y^2+140x+100=0#

rectangular and polar form are related as follows:

#x= r cos theta# and #y= rsin theta#, so #r^2= x^2 +y^2#

Accordingly, the given expression can be reworked as follows:

#4r -7rcos theta=10#

#4r= 10+7x# Square both sides,

#16r^2= (10+7x)^2#

#16x^2+16y^2= 100+140x +49x^2#

#33x^2 -16y^2+140x+100=0#