Question

The transformed equation of $x^2+2y^2+2x-4y+2=0$ when origin is shifted to the point $(-1,1)$ with out rotation of axes, is

• A. $X^2-2Y^2=1$
• B. $X^2+2Y^2=1$
• C. $2X^2+Y^2=1$
• D. $X^2-Y^2=0$

Answer 1

The correct option is B $X^2+2Y^2=1$

Original equation is $x^2+2y^2+2x-4y+2=0$
Origin is shifted to $(-1,1)$
$\therefore x=X+h=X-1y=Y+k=Y+1$
Transformed equation is
$(X-1{)}^2+2(Y+1{)}^2+2(X-1)-4(Y+1)+2=0\Rightarrow X^2-2X+1+2Y^2+4Y+2+2X-2-4Y-4+2=0\Rightarrow X^2+2Y^2=1$