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

The transformed equation of $x^2-y^2+2 x+4 y=0$ when the origin is shifted to the point $(-1,2)$ is
  1. $x^2+y^2=1$
  2. $x^2+3 y^2=1$
  3. $x^2-y^2+3=0$
  4. $4 x^2+9 y^2=36$

Solution

$x^2-y^2+2 x+4 y=0$
Origin is shifted to $(-1,2)$, Let $x=X-1, y=Y+2$ $\begin{aligned} & \Rightarrow(X-1)^2-(Y+2)^2+2(X-1)+4(Y+2)=0 \\ & \Rightarrow X^2-Y^2+3=0 \end{aligned}$

Asked in: AP EAMCET 2024 (22 May Shift 1)

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