JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
A hyperbola passes through the point \(P\left( {\sqrt 2 ,\sqrt 3 } \right)\) has foci at \(\left( { \pm 2,0} \right)\). Then the tangent to this hyperbola at \(P\) also passes through the point
- A \(\left( { - \sqrt 2 , - \sqrt 3 } \right)\)
- B \(\left( {3\sqrt 2 ,2\sqrt 3 } \right)\)
- C \(\left( {2\sqrt 2 ,3\sqrt 3 } \right)\)
- D \(\left( {3,\sqrt 2 } \right)\)
Answer & Solution
Correct Answer
(C) \(\left( {2\sqrt 2 ,3\sqrt 3 } \right)\)
Step-by-step Solution
Detailed explanation
Equation of hyperbola is \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) foci is \((\pm 2,0) \Rightarrow a c=2 \Rightarrow a^{2} c^{2}=4\) Since \(b^{2}=a^{2}\left(e^{2}-1\right)\) \(b^{2}=a^{2} e^{2}-a^{2}\) \(\therefore \quad a^{2}+b^{2}=4\) .......\((1)\) Hyperbola passes…
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