theamatthechi
theamatthechi theamatthechi
  • 14-08-2016
  • Mathematics
contestada

Convert the polar equation to rectangular form:

r = 2 / [1 + sin(theta)]

Respuesta :

metchelle
metchelle metchelle
  • 17-08-2016
R = 2 / (1 + sin θ)

Using the following relations:

R = sqrt (x^2 + y^2)
sin θ = y/R

R = 2 / (1 + y/R)
R(1 + y/R) = 2
R + y = 2
R = 2 - y
sqrt(x^2 + y^2) = 2 - y

Squaring both sides:
x^2 + y^2 = (2 - y)^2
x^2 + y^2 = 4 - 4y + y^2

x^2 + 4y - 4 
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