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 \[{{\left( x\pm 2 \right)}^{2}}+{{\left( y\pm 4 \right)}^{2}}=20\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}\pm 4x\pm 8y=0\]