Q56 / 155 · WBJEE 2023 · Mathematics

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

  • Correct answer
    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
    \(y=x \sqrt{3}+\sqrt{6}\)

Solution

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 \(\sqrt{6 x}-y=\sqrt{3}\)

Hence, the correct answer is option: 'A'.

More Hyperbola Questions