JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(P (3\, sec\,\theta , 2\, tan\,\theta )\) and \(Q\, (3\, sec\,\phi , 2\, tan\,\phi )\) where \(\theta + \phi \, = \frac{\pi}{2}\) , be two distinct points on the hyperbola \(\frac{{{x^2}}}{9} - \frac{{{y^2}}}{4} = 1\) . Then the ordinate of the point of intersection of the normals at \(P\) and \(Q\) is
- A \(\frac{11}{3}\)
- B \(-\frac{11}{3}\)
- C \(\frac{13}{2}\)
- D \(-\frac{13}{2}\)
Answer & Solution
Correct Answer
(D) \(-\frac{13}{2}\)
Step-by-step Solution
Detailed explanation
Let the coordinate at point of intersection of normal at \(P\) and \(Q\) be \((h,k)\) Since, equation of normal to the hyperbola \(\,\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}} = 1\) At point \(\left( {{x_1},{y_1}} \right)\) is…
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