After the rotation of the coordinate axes with given angle the relation between new (X,Y) and old coordinates (x,y) is given by, (x,y)=[Xcosθ−Ysinθ],(Ycosθ+Xsinθ) The angle is θ=
π
4
Then, (x,y)=(
X
√2
−
Y
√2
),(
Y
√2
+
X
√2
) So 25(
X−Y
√2
)2+9(
X+Y
√2
)2=225 34X2+34Y2−32XY=450 17X2+17Y2−16XY=225 Comparison of the coefficients gives, α=γ=17,β=−16,δ=225 This implies, (α+β+γ−√δ)2=(34−16−15)2 =32 =9