Match the column: (A) Number of integral values of \( b \) for which tangent parallel to Column ...

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Match the column:
(A) Number of integral values of \( b \) for which tangent parallel to
Column - II
(p) 16
P
line \( y=x+1 \) can be drawn to hyperbola \( \frac{x^{2}}{5}-\frac{y^{2}}{b^{2}}=1 \) is
W
(B) The equation of the hyperbola with vertices \( (3,0) \) and \( (-3,0) \)
(q) 4 and semi-latusrectum 4 , is given by is \( 4 x^{2}-3 y^{2}=4 k \), then \( k= \)
(C) The product of the lengths of the perpendiculars
(r) 3 from the two focii on any tangent to the hyperbola \( \frac{x^{2}}{25}-\frac{y^{2}}{3}=1 \) is \( \sqrt{k} \), then \( k \) is
(D) An equation of a tangent to the hyperbola,
(s) \( \quad 9 \) \( 16 x^{2}-25 y^{2}-96 x+100 y-356=0 \) which makes an angle \( \frac{\pi}{4} \) with the transverse axis is \( y=x+1,(10) \), then 21 is
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