A) \[{{p}^{2}}=2\]
B) \[{{p}^{2}}=5\]
C) \[5{{p}^{2}}=2\]
D) \[2{{p}^{2}}=5\]
Correct Answer: D
Solution :
The condition for the line \[y=mx+c\] will touch the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is \[{{c}^{2}}={{a}^{2}}{{m}^{2}}\]\[-{{b}^{2}}\] Here \[m=-1\], \[c=\sqrt{2}p,\] \[{{a}^{2}}=9,\,\,{{b}^{2}}=4\] \ We get \[2{{p}^{2}}=5.\]
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