AP EAMCET · Maths · Hyperbola
A hyperbola passes through the point \(\mathrm{P}(\sqrt{2}, \sqrt{3})\) and has foci at \(( \pm 2,0)\). Then the point that lies on the tangent drawn to this hyperbola at P is
- A \((\sqrt{3}, \sqrt{2})\)
- B \((-\sqrt{2},-\sqrt{3})\)
- C \((2 \sqrt{2}, 3 \sqrt{3})\)
- D \((3 \sqrt{2}, 2 \sqrt{3})\)
Answer & Solution
Correct Answer
(C) \((2 \sqrt{2}, 3 \sqrt{3})\)
Step-by-step Solution
Detailed explanation
\(c^2 = 2^2 = 4\) \(a^2 + b^2 = 4\) \(\frac{(\sqrt{2})^2}{a^2} - \frac{(\sqrt{3})^2}{b^2} = 1 \Rightarrow \frac{2}{a^2} - \frac{3}{b^2} = 1\) \(\frac{2}{a^2} - \frac{3}{4 - a^2} = 1 \Rightarrow 2(4 - a^2) - 3a^2 = a^2(4 - a^2)\)…
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