Question: The condition for existence of three real normals drawn to a parabola y 2 = 4 ax from a given point ( h, k ) are given below; Condition-1: h 2 a and Condition-2: 27 ak 2 h - 2 a ) 3 . What is difference in the two conditions so obtained/ or which one is more correct?

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Question: The condition for existence of three real normals drawn to a parabola y 2 = 4 ax from a given point ( h, k ) are given below; Condition-1: h > 2 a and Condition-2: 27 ak 2 h - 2 a ) 3 . What is difference in the two conditions so obtained/ or which one is more correct?

Harshit Singh · Answer

Dear Student
Difference in both methods is that in method 1 , condition for real roots has been applied while in second method,different method of putting points and checking their sign has been used along with condition of stationary point.

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Question: The condition for existence of three real normals drawn to a parabola y 2 = 4 ax from a given point ( h, k ) are given below; Condition-1: h > 2 a and Condition-2: 27 ak 2 h - 2 a ) 3 . What is difference in the two conditions so obtained/ or which one is more correct?

Question: The condition for existence of three real normals drawn to a parabola y² **= 4ax from a given point (h, k) are given below;
Condition-1: h > 2a and
Condition-2: 27ak² h - 2a)³.
What is difference in the two conditions so obtained/ or which one is more correct?**

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Question: The condition for existence of three real normals drawn to a parabola y 2 = 4 ax from a given point ( h, k ) are given below; Condition-1: h > 2 a and Condition-2: 27 ak 2 h - 2 a ) 3 . What is difference in the two conditions so obtained/ or which one is more correct?

Question: The condition for existence of three real normals drawn to a parabola y2 = 4ax from a given point (h, k) are given below; Condition-1: h > 2a and Condition-2: 27ak2 h - 2a)3.What is difference in the two conditions so obtained/ or which one is more correct?

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Question: The condition for existence of three real normals drawn to a parabola y² **= 4ax from a given point (h, k) are given below;
Condition-1: h > 2a and
Condition-2: 27ak² h - 2a)³.
What is difference in the two conditions so obtained/ or which one is more correct?**