TS EAMCET · Maths · Hyperbola
Let \(\mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S}\) be the points of intersection of the circle \(x^2+y^2=4\) and the hyperbola \(x y=\sqrt{3}\). If \(\mathrm{P}=(\alpha, \beta)\) and \(\alpha>\beta>0\), then the equation of the tangent drawn at P to the hyperbola is
- A \(x+y=2\)
- B \(x+\sqrt{3} y=2 \sqrt{3}\)
- C \(\sqrt{3} x+y=\sqrt{3}\)
- D \(x-y=0\)
Answer & Solution
Correct Answer
(B) \(x+\sqrt{3} y=2 \sqrt{3}\)
Step-by-step Solution
Detailed explanation
\(x^2 + \left(\frac{\sqrt{3}}{x}\right)^2 = 4 \Rightarrow x^4 - 4x^2 + 3 = 0 \Rightarrow (x^2-1)(x^2-3)=0\) \(x^2=1 \Rightarrow x=\pm 1, y=\pm \sqrt{3}\). \(x^2=3 \Rightarrow x=\pm \sqrt{3}, y=\pm 1\) Points of intersection:…
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