The equationλ2x2+λ2−5λ+4xy+(3λ−2)y2−8x+12y−4=0will represent a circle, if λ=

The given equation will represent a circle, ifCoeff. of x2= Coeff of y2 and Coeff. of xy=0.⇒ λ2=3λ−2 and λ2−5λ+4=0⇒λ2−3λ+2=0 and λ2−5λ+4=0⇒ (λ−1)(λ−2)=0 and (λ−1)(λ−4)=0⇒ λ=1