Question

when the origin is shifted (-1,2) by the translation of axes , find the transformed equation of the 2x²+y²-4x+4y=0 ​

Answer 1

Step-by-step explanation:

Let the new coordinates of any point be $(X,Y)$ and origin is $(-1,2)$

So,

$x = X - 1 \\ y =Y + 2$

Now, put these values in the given equation,

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

$\implies2(X^{2} - 2 X + 1)+ (Y^{2} + 4Y + 4) - 4X + 4 + 4 Y + 8 = 0$

$\implies2X^{2} - 4X + 2+ Y^{2} + 4Y + 4 - 4X + 4 + 4 Y + 8 = 0$

$\implies2X^{2} + Y^{2} - 8X + 8Y + 2 + 4 + 4 + 8 = 0$

$\implies2X^{2} + Y^{2} - 8X + 8Y + 18 = 0$