TG EAMCET 3 May 2025 Shift 2 Paper

Question : 42 of 160

Marks: +1, -0

By shifting the origin to the point (−1,2) through translation of axes, if ax2+2hxy+by2+2gx+2fy+c=0 is the transformed equation of 2x2−xy+y2−3x+4y−5=0, then 2(f+g+h)=

‌a+b+c
‌a−5(b+c)
‌3(a+b+c)
‌c−5(a+b)

Validate

X=x−h,Y=y−k
X=x+1,Y=y−2
x=X−1,y=Y+2
⇒‌‌2(X−1)2−(X−1)(Y+2)+(Y+2)2−3(X−1)+4(Y+2)−5=0
⇒‌‌2X2−4X+2−XY−2X+Y+2
‌‌begin‌array‌rl‌‌+Y2+4y+4‌\‌‌−3X+3+4Y+8−5=0‌a=2
2h=−1‌b=1 2g=−4−2−3=−9‌‌‌c=2+2+4+3+8−5 2f=1+4+4=9‌‌=14
2(f+g+h)=−1
And c−5(a+b)=14−15=−1

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