question_answer

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) \[{{x}^{2}}+{{y}^{2}}\pm 4x\pm 8y=0\]

B) \[{{x}^{2}}+{{y}^{2}}\pm 2x\pm 4y=0\]

C) \[{{x}^{2}}+{{y}^{2}}\pm 8x\pm 16y=0\]

D) \[{{x}^{2}}+{{y}^{2}}\pm x\pm y=0\]

Correct Answer: A

Solution :

In\[\Delta OAC\],\[O{{C}^{2}}={{2}^{2}}+{{4}^{2}}=20\] \[\therefore \]Required equation of circle is                 \[{{(x\pm 2)}^{2}}+{{(y\pm 4)}^{2}}=20\] \[\Rightarrow \]               \[{{x}^{2}}+{{y}^{2}}\pm 4x+8y=0\]