A) \[-1\]
B) \[1\]
C) \[{{c}^{4}}\]
D) \[-{{c}^{4}}\]
Correct Answer: B
Solution :
Parametric equation of the hyperbola \[xy={{c}^{2}}\]is \[(ct,\,c/t)\] and equation of circle is \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] ?..(i) Put \[x=ct\] and \[y=c/t\]in (i) \[{{(ct)}^{2}}+{{\left( \frac{c}{t} \right)}^{2}}={{a}^{2}}\] \[{{c}^{2}}{{t}^{4}}+{{c}^{2}}-{{a}^{2}}{{t}^{2}}=0\] ?..(ii) From (ii), \[{{t}_{1}}\,{{t}_{2}}\,{{t}_{3}}\,{{t}_{4}}=\frac{{{c}^{2}}}{{{c}^{2}}}=1\]You need to login to perform this action.
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