convert r=2sintheta-4costheta to rectangular form

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Let r^2 = x^2 + y^2 Let rsin(theta) = y Let rcos(theta) = x r = 2sintheta - 4costheta Multiply both sides by r. r*r = r(2sintheta - 4costheta) r^2 = 2rsin(theta) - 4rcos(theta) Make the substitution given above. x^2 + y^2 = 2y - 4x Set equation to zero. x^2 + y^2 + 4x - 2y = 0 It is the equation of a circle.