What is the polar form of the equation: x^2+y^2 =xy+1
Using Pythagoras, x2 + y2 = r2.Using basic trigonometry, x = rsinθ and y = rcosθ.
xy + 1 = r2sinθcosθ + 1 = (1/2)r2sin2θ + 1
Subbing in both halves and doubling gives:2r2 = r2sin2θ + 2
-> r2(2 - sin2θ)r2 = 2
-> r2 = 2/(2-sin2θ)
HW
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