TS EAMCET 9 May 2024 Shift 1 Solved Paper

When origin is shifted to (2,b) by translation of axes, the coordinates of the point (a,4) have changed to (6,8)
∴X=x−2⇒Y=y−b
For point (a,4) transforming to (6,8)
6=a−2⇒a=8
8=4−b⇒b=−4
So, the point (a,b) is (8,−4).
Now, when origin is shifted to (a,b)
⇒‌‌X=x−8⇒Y=y+4
and transformed equation of x2+4xy+y2=0 is
‌(X+8)2+4(X+8)(Y−4)+(Y−4)2=0
‌X2+Y2+4XY+24Y−48=0
On comparing with
X2+2HXY+Y2+2GX+2FY+C=0
we get, G=0,H=2,F=12,C=−48
∴2H(G+F)=2×2(0+12)=48=−C