Question

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

• 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 $

Answer 1

Answer: (A)

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 $