Question

Shift the origin to a suitable point so that the equation $y^2+4y+8x-2=0$ will not contain $y$ and constant terms is

• A. $(3/4,-2)$
• B. $(3/4,2)$
• C. $(2,3/4)$
• D. $(2,-3/4)$

Answer 1

The correct option is A $(3/4,-2)$

$y^2+4y+8x-2=0$

$y^2+2\cdot \left(2\right)\cdot y+4-4=2-8x$

${(y+2)}^2=6-8x$

${(y+2)}^2=8(\frac{6}{8}-x)$

${(y+2)}^2=8(\frac{3}{4}-x)$

Now, equation will become-

$Y^2=8X$

Here $Y=y+2X=\frac{3}{4}-x$

At $(0,0),\Rightarrow (X,Y)=(\frac{3}{4},-2)$