What is the polar form of the equation? (x+6)^2+y^2=36
To change from rectangular to polar, replace x with r·cos(theta) and y with r·sin(theta).
(x + 6)2 + y2 = 36 -----> ( r·cos(theta) + 6 )2 + ( r·sin(theta) )2 = 36
Multiplying out: r2·cos2(theta) + 12·r·cos(theta) + 36 + r2·sin(theta) = 36
Subtracting 36: r2·cos2(theta) + 12·r·cos(theta) + r2·sin(theta) = 0
Rearranging: r2·cos2(theta) + r2·sin(theta) + 12·r·cos(theta) = 0
Factoring: r2( cos2(theta) + r2·sin(theta) ) + 12·r·cos(theta) = 0
Since cos2 + sin2 = 1: r2 + 12·r·cos(theta) = 0
Factoring: r( r + 12·cos(theta) ) = 0