a=(x,2,−1)b=(6,−y,2) If |a×b|2+|a⋅b|2=f(x)g(y) =|a|2|b|2sin2θ+|a|2|b|2cos2θ =|a|2|b|2(sin2θ+cos2θ)=|a|2|b|2 =(x2+4+1)(36+y2+4) =(x2+5)(y2+40)=f(x)g(x) f(x)=x2+5 and g(x)=y2+40 f(x)+g(x)−46=0 ⇒x2+5+y2+40−46=0 ⇒x2+y2−1=0 ⇒x2+y2=1 This is the equation of circle.