A) \[{{y}_{1}}+{{y}_{2}}+{{y}_{3}}=0\]
B) \[{{x}_{1}}{{x}_{2}}+{{x}_{2}}{{x}_{2}}+{{x}_{3}}{{x}_{1}}=0\]
C) \[{{x}_{1}}+{{x}_{2}}+{{x}_{3}}=0\]
D) \[{{x}_{1}}{{y}_{1}}+{{x}_{2}}{{y}_{2}}+{{x}_{3}}{{y}_{3}}=0\]
Correct Answer: A
Solution :
If the normal to the parabola \[{{x}^{2}}=-4ay\] at the points \[({{x}_{1}},{{y}_{1}}),\,({{x}_{2}},{{y}_{2}})\] and \[({{x}_{3}},{{y}_{3}})\]are concurrent, then sum of ordinate is zero. ie, \[{{y}_{1}}+{{y}_{2}}+{{y}_{3}}=0\]
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