How do you convert #-x^2+2xy-y^2=9# into polar form?
1 Answer
Feb 9, 2016
# 9/(sin2theta-1) #
Explanation:
using the formulae which link Cartesian to Polar coordinates
# • r^2 = x^2 + y^2 #
#• x = rcostheta #
# • y = rsintheta # rewrite as
# -x^2 - y^2 + 2xy = 9 # so -
# (x^2 +y^2) + 2xy = 9 # hence
# - r^2 + 2( rcostheta.rsintheta) =9 # and
# -r^2 + 2r^2 costhetasintheta =9 # common factor:
# r^2 (2costhetasintheta-1 )= 9 # (Note that :
# sin2theta = 2costhetasintheta # )hence
#r^2(sin2theta - 1 ) = 9#
# rArr r^2 = 9/(sin2theta -1) #
