TS EAMCET · Maths · Circle
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 \(x^2+y^2 \pm 4 x \pm 8 y=0\)
- B \(x^2+y^2 \pm 2 x \pm 4 y=0\)
- C \(x^2+y^2 \pm 8 x \pm 16 y=0\)
- D \(x^2+y^2 \pm x \pm y=0\)
Answer & Solution
Correct Answer
(A) \(x^2+y^2 \pm 4 x \pm 8 y=0\)
Step-by-step Solution
Detailed explanation
In \(\triangle O A C, \quad O C^2=2^2+4^2=20\) \(\therefore\) Required equation of circle is \(\begin{aligned} & (x \pm 2)^2+(y \pm 4)^2=20 \\ \Rightarrow \quad & x^2+y^2 \pm 4 x \pm 8 y=0 \end{aligned}\)
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