AP EAMCET · Maths · Circle
For different real non-zero numbers \(x_1, x_2, x_3\) and \(x_4\), suppose the points \(\left(x_1, \frac{1}{x_1}\right),\left(x_2, \frac{1}{x_2}\right),\left(x_3, \frac{1}{x_3}\right)\) and \(\left(x_4, \frac{1}{x_4}\right)\) lie on the boundary of a circle of radius 4 . Then, the value of \(x_1 x_2 x_3 x_4\) is
- A \(1\)
- B \(2\)
- C \(4\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
Let the equation of the circle be \(x^2+y^2+2 g x+2 f y+c=0\) \(\left(x_i, \frac{1}{x_i}\right)\) lies on the above circle. \(\therefore \quad x_i^2+\frac{1}{x_i^2}+2 g x_i+\frac{2 f}{x_i}+C=0\)…
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