Question

If the origin is shifted to the point $(2,-1)$, obtain the new equation of the locus $2x^2+3xy-9y^2-5x-24y-7=0$, axes remaining parallel.

Answer 1

Origin is shiftef to $(2,-1)$

=>For transformed equation replace $x\stackrel{}{\to }x-2$ and $y\stackrel{}{\to }y+1$

Now equation =>$2(x-2{)}^2+3(x-2\left)\right(y+1)-9{(y+1)}^2-5(x-2)-24(y+1)-7=0=>{2x}^2-10x+3xy-48y-{9y}^2-28=0$