Question:

The equations of the circle which pass through the origin and makes intercepts of lengths 44 and 88 on the xx and yy-axes respectively are

Updated On: Feb 15, 2025
  • x2+y2±4x±8y=0x^{2}+y^{2}\pm4x\pm8y=0
  • x2+y2±2x±4y=0x^{2}+y^{2}\pm2x\pm4y=0
  • x2+y2±8x±16y=0x^{2}+y^{2}\pm8x\pm16y=0
  • x2+y2±x±y=0x^{2}+y^{2}\pm x\pm y=0
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The Correct Option is A

Solution and Explanation

In ΔOAC,    OC2=22+42=20\Delta O A C, \,\,\,\,O C^{2}=2^{2}+4^{2}=20

\therefore Required equation of circle is
(x±2)2+(y±4)2=20(x \pm 2)^{2}+(y \pm 4)^{2} =20
x2+y2±4x±8y=0\Rightarrow x^{2}+y^{2} \pm 4 x \pm 8 y =0
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