Q97 / 160 · AP EAMCET 2023 (18 May Shift 1) · Mathematics

The equation of the pair of asymptotes of the hyperbola $x^2-2 y^2-8 x+8 y+4=0$ is

  • A
    $x^2-2 y^2-8 x+8 y-8=0$
  • B
    $2 x^2-4 y^2-16 x+16 y-7=0$
  • Correct answer
    C
    $x^2-2 y^2-8 x+8 y+8=0$
  • D
    $2 x^2-4 y^2-16 x+16 y+9=0$

Solution

$\because x^2-2 y^2-8 x+8 y+4=0$ $\begin{aligned} & \Rightarrow \quad(x-4)^2-2(y-2)^2-16 \\ & \Rightarrow \quad(x-4)^2-2(y-2)^2=4\end{aligned}$ Then, the equation of asymptote is $\begin{aligned} & \left(x^2-4\right)^2-2(y-2)^2=0 \\ & \Rightarrow \quad x^2+16-8 x-2 y^2+8 y-8=0 \\ & \Rightarrow \quad x^2-2 y^2-8 x+8 y+8=0\end{aligned}$

Hence, the correct answer is option: 'C'.

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