Question #893e2

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Answer 1 · 2017-06-01T12:41:29

#r^2=2/(1-2sin2theta)#

for polar /rectangular conversions there are three transformation equations

#color(red)(x^2+y^2=r^2)#

#color(blue)(x=rcostheta)#

#color(green)(y=rsintheta)#

for #color(red)(x^2+y^2)-4color(blue)(x)color(green)(y)=2#

we will need all three formulae

#color(red)(r^2)-4color(blue)(rcostheta)color(green)(rsintheta)=2#

now we simplify, and tidy up

#r^2-4r^2sinthetacostheta=2#

using

#sin2theta=2sinthetacostheta#

#r^2(1-2sin2theta)=2#

#r^2=2/(1-2sin2theta)#