AP EAMCET Engineering 20 Apr 2019 Shift 1 Paper

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