The equations of the circle which pass through the origin and makes intercepts of lengths 4 and 8 on the $x$…

The equations of the circle which pass through the origin and makes intercepts of lengths 4 and 8 on the $x$ and $y$-axes respectively are
  1. $x^2+y^2 \pm 4 x \pm 8 y=0$
  2. $x^2+y^2 \pm 2 x \pm 4 y=0$
  3. $x^2+y^2 \pm 8 x \pm 16 y=0$
  4. $x^2+y^2 \pm x \pm y=0$

Solution

In $\triangle O A C, \quad O C^2=2^2+4^2=20$
$\therefore$ Required equation of circle is $\begin{aligned} & (x \pm 2)^2+(y \pm 4)^2=20 \\ \Rightarrow \quad & x^2+y^2 \pm 4 x \pm 8 y=0 \end{aligned}$

Asked in: AP EAMCET 2009

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