Let $$P(a\sec \theta ,\ b\tan \theta )$$ and $$Q(a\sec \varphi ,\ b\tan \varphi )$$, where $$\theta +\varphi =\frac{\pi }{2}$$, be two points on the hyperbola $$\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$$. If (h, k) is the point of intersection of the normals at P and Q, then k is equal to [IIT 1999; MP PET 2002]

Question

Let $$P(a\sec \theta ,\ b\tan \theta )$$ and $$Q(a\sec \varphi ,\ b\tan \varphi )$$, where $$\theta +\varphi =\frac{\pi }{2}$$, be two points on the hyperbola $$\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1$$. If (h, k) is the point of intersection of the normals at P and Q, then k is equal to                                                                            [IIT 1999;  MP PET 2002]

TuteeHUB · Accepted Answer

NA

TuteeHUB · Answer

$$\frac{{{a}^{2}}+{{b}^{2}}}{a}$$

TuteeHUB · Answer

$$-\left( \frac{{{a}^{2}}+{{b}^{2}}}{a} \right)$$

TuteeHUB · Answer

$$\frac{{{a}^{2}}+{{b}^{2}}}{b}$$

TuteeHUB · Answer

$$-\left( \frac{{{a}^{2}}+{{b}^{2}}}{b} \right)$$

1.	Let \[P(a\sec \theta ,\ b\tan \theta )\] and \[Q(a\sec \varphi ,\ b\tan \varphi )\], where \[\theta +\varphi =\frac{\pi }{2}\], be two points on the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]. If (h, k) is the point of intersection of the normals at P and Q, then k is equal to [IIT 1999; MP PET 2002]
A.	\[\frac{{{a}^{2}}+{{b}^{2}}}{a}\]
B.	\[-\left( \frac{{{a}^{2}}+{{b}^{2}}}{a} \right)\]
C.	\[\frac{{{a}^{2}}+{{b}^{2}}}{b}\]
D.	\[-\left( \frac{{{a}^{2}}+{{b}^{2}}}{b} \right)\]
Answer» E.

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