AP EAMCET · Maths · Circle
If the intercepts made by a variable circle on the X -axis and Y -axis are 8 and 6 units respectively, then the locus of the centre of the circle is
- A \(x^2-y^2+28=0\)
- B \(y^2-x^2-7=0\)
- C \(x^2-y^2-28=0\)
- D \(x^2-y^2-7=0\)
Answer & Solution
Correct Answer
(D) \(x^2-y^2-7=0\)
Step-by-step Solution
Detailed explanation
\(2\sqrt{r^2 - k^2} = 8 \Rightarrow r^2 - k^2 = 16\) \(2\sqrt{r^2 - h^2} = 6 \Rightarrow r^2 - h^2 = 9\) \(16 + k^2 = 9 + h^2\) \(h^2 - k^2 = 7\) \(x^2 - y^2 - 7 = 0\)
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