How do you convert #x^2 + 5xy + y^2 = 7# to polar form?

1 Answer
Jim G.
May 1, 2016

#r^2=7/(1+5/2sin2theta)#

Explanation:

To convert from Cartesian to Polar coordinates use the following formulae which link them.

#• x=rcostheta , y=rsintheta #

#rArr r^2cos^2theta+5r^2costhetasintheta+r^2sin^2theta=7#

remove the common factor of #r^2#

#rArrr^2(cos^2theta+5costhetasintheta+sin^2theta)=7#

Simplify using trig. identities

#• sin^2theta+cos^2theta=1" and "#

#• sin2theta=2sinthetacostheta#

#rArrr^2(1+5/2sin2theta)=7#

#rArrr^2=7/(1+5/2sin2theta)#

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