How do you convert #r = 1/(1-cos(theta))# into cartesian form?

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Answer 1 · 2016-08-09T14:34:27

#y^2=2x+1# representing the parabola with axis ax =-1/2 and focus at the origin.

The conversion formula is #(x, y) = (rcos theta, rsin theta)#.

The given equation is #r = sqrt (x^2+y^2)=1/(1-x/sqrt(x^2+y^2)#

Cross multiplying, rationalizing and simplifying,

#y^2=2x+1#

#(y-beta)^2=4a(s-alpha)#,

representing parabolas having vertex at #(alpha, beta) parameter a

and focus at(#alpha +a, beta)#.

Here, #a = 1/2, alpha = -1/2 and beta = 0#...