Question

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

Answer 1

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

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
$Y^2=4aX$
$\Rightarrow 4a=8$
$\Rightarrow a=2$