A variable chord of the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2...

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A variable chord of the hyperbola \( \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1,(ba) \),
\( \mathrm{P} \) subtends a right angle at the center of the hyperbola if this

W chord touches
(1) a fixed circle concentric with the hyperbola
(2) a fixed ellipse concentric with the hyperbola
(3) a fixed hyperbola concentric with the hyperbola
(4) a fixed parabola having vertex at \( (0,0) \)
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