WBJEE · Maths · Hyperbola
If a hyperbola passes through the point \(\mathrm{P}(\sqrt{2}, \sqrt{3})\) and foci at \(( \pm 2,0)\) then the tangent to this hyperbola at \(\mathrm{P}\) is
- A \(\mathrm{y}=\mathrm{x} \sqrt{6}-\sqrt{3}\)
- B \(\mathrm{y}=\mathrm{x} \sqrt{3}-\sqrt{6}\)
- C \(\mathrm{y}=\mathrm{x} \sqrt{6}+\sqrt{3}\)
- D \(y=x \sqrt{3}+\sqrt{6}\)
Answer & Solution
Correct Answer
(A) \(\mathrm{y}=\mathrm{x} \sqrt{6}-\sqrt{3}\)
Step-by-step Solution
Detailed explanation
Hint: \(a e=2, a^2+b^2=4\) \(\Rightarrow \frac{2}{a^2}-\frac{3}{b^2}=1 \Rightarrow b^2=3 ; a^2=1\) \(\frac{x^2}{1}-\frac{y^2}{3}=1\). Tangent at \(P(\sqrt{2}, \sqrt{3})\) is \(\sqrt{6 x}-y=\sqrt{3}\)
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