A) \[{{t}_{2}}=2{{t}_{1}}\]
B) \[{{t}_{2}}+2{{t}_{1}}=0\]
C) \[{{t}_{1}}+2{{t}_{2}}=0\]
D) None of these
Correct Answer: B
Solution :
[b] \[A\left( at_{1}^{2},2a{{t}_{1}} \right)\]and \[B\left( at_{2}^{2},2a{{t}_{2}} \right)\]are such that AC : AB = 1 : 3 \[\therefore C\left( \frac{2at_{1}^{2}+at_{2}^{2}}{3},\frac{4a{{t}_{1}}+2a{{t}_{2}}}{3} \right)\] Point C lies on x-axis then \[\frac{4a{{t}_{1}}+2a{{t}_{2}}}{3}=0\] \[\Rightarrow {{t}_{2}}+2{{t}_{1}}=0\]
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