How do you convert #r^2 = cost# to rectangular form?

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Answer 1 · 2016-12-04T17:43:59

#(x^2+y^2)^(3/2)-x =0#

We have:

#x=rcost#
#y=rsint#

and from this we can derive:

#x^2+y^2 = r^2#

#cost = x/r =+- x/sqrt(x^2+y^2)#

We can se from the equation that #cost#must always be positive (as it equals #r^2#), so we take the positive sign of the square root, and have:

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

or:

#(x^2+y^2)^(3/2)-x =0#