How do you convert #x^2/36 + y^2/100 = 1 # into polar form?

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Answer 1 · 2016-11-24T20:00:16

Please see the explanation.

Substitute #rsin(theta)# for y and #rcos(theta)# for x:

#(rcos(theta))^2/36 + (rsin(theta))^2/100 = 1#

Factor out #r^2#

#r^2(cos^2(theta)/36 + sin^2(theta)/100) = 1#

Make a common denominator:

#r^2(100cos^2(theta) + 36sin^2(theta))/3600 = 1#

#r^2(64cos^2(theta) + 36cos^2(theta) + 36sin^2(theta))/3600 = 1#

#r^2(64cos^2(theta) + 36)/3600 = 1#

Divide both side by #(64cos^2(theta) + 36)/3600#:

#r^2 = 3600/(64cos^2(theta) + 36)#

square root both sides:

#r = 60/sqrt(64cos^2(theta) + 36)#