A) \[{{t}_{1}}{{t}_{2}}={{t}_{3}}{{t}_{4}}\]
B) \[{{t}_{1}}{{t}_{2}}{{t}_{3}}{{t}_{4}}=1\]
C) \[{{t}_{1}}={{t}_{2}}\]
D) \[{{t}_{3}}={{t}_{4}}\]
Correct Answer: B
Solution :
Let equation of circle is \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] Parametric form of \[xy={{c}^{2}}\] are \[x=ct,\,\,\,y=\frac{c}{t}\] Þ \[{{c}^{2}}{{t}^{2}}+\frac{{{c}^{2}}}{{{t}^{2}}}={{a}^{2}}\] Þ \[{{c}^{2}}{{t}^{4}}-{{a}^{2}}{{t}^{2}}+{{c}^{2}}=0\] Product of roots will be, \[{{t}_{1}}{{t}_{2}}{{t}_{3}}{{t}_{4}}=\frac{{{c}^{2}}}{{{c}^{2}}}=1\].You need to login to perform this action.
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