Question

The origin is shifted to $(1,2)$, the equation $y^2-8x-4y+12=0$ changes to $Y^2+4aX=0$, then $a$ is equal to

• A. $2$
• B. $-2$
• C. $1$
• D. $-1$

Answer 1

The correct option is B $-2$

Given equation $y^2-8x-4y+12=0$

Let the coordinates of any point $(x,y)$ on the given line changes to $(X,Y)$ on shifting the origin to $(1,2)$.

So $x=X+1,y=Y+2$

So, the transformed equation is

$(Y+2{)}^2-8(X+1)-4(Y+2)+12=0$

$\Rightarrow Y^2+4Y+4-8X-8-4Y-8+12=0$

$\Rightarrow Y^2=-8X$

Comparing with the given transformed equation

$Y^2=-4aX$

$\Rightarrow 4a=-8$

$\Rightarrow a=-2$