Question

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

• A. $x^{2}+y^{2}\pm4x\pm8y=0$
• B. $x^{2}+y^{2}\pm2x\pm4y=0$
• C. $x^{2}+y^{2}\pm8x\pm16y=0$
• D. $x^{2}+y^{2}\pm x\pm y=0$

Answer 1

Answer: (A)

$x^{2}+y^{2}\pm4x\pm8y=0$

Answer 2

In $\Delta O A C, \,\,\,\,O C^{2}=2^{2}+4^{2}=20$

$\therefore$ Required equation of circle is
$(x \pm 2)^{2}+(y \pm 4)^{2} =20$
$\Rightarrow x^{2}+y^{2} \pm 4 x \pm 8 y =0$