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Question #0f0cb

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Dec 16, 2016

#(x^2 +y^2)^3= 9(x^2 -y^2)^2#

Explanation:

Write the given equation as #r=3(cos^2 theta - sin^2 theta)#

Or #r^3= 3 (r^2 cos^2 theta -r^2 sin^2 theta)#

Since #r^2 = x^2 +y^2# and #rcos theta =x, and rsin theta =y#,

it would be #(x^2+y^2)^(3/2) = 3(x^2- y^2)#

Now square both sides. #(x^2 +y^2)^3= 9(x^2 -y^2)^2#

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