How do you graph # r = 2 /( 1- sintheta)#?

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Answer 1 · 2018-03-15T09:45:36

Draw a graph of #y=x^2# that is lowered by 4 units and have all #y#-values quartered (squished by x4)

Multiply each side by #r(1-sintheta)# to get:
#r^2-r^2sintheta=2r#

#r^2-r(rsintheta)=2r#

#r^2=x^2+y^2#
#r=sqrt(x^2+y^2)#
#rsintheta=y#

#x^2+y^2-ysqrt(x^2+y^2)=2sqrt(x^2+y^2)#

#x^2+y^2=sqrt(x^2+y^2)(2+y)#

#2+y=(x^2+y^2)/sqrt(x^2+y^2)=sqrt(x^2+y^2)#

#4+4y+y^2=x^2+y^2#

#y=(x^2-4)/4#

Draw a graph of #y=x^2# that is lowered by 4 units and have all #y#-values quartered (squished by x4):
graph{(x^2-4)/4 [-5, 5, -2, 5]}