Paragraph: Read the following write up carefully and answer the following questions: Consider a parabola, y ^2=4 ax then y + tx = at ^3+2 at represents a normal at a point (at ^2, 2 a t ). It can also be represented as y-m x+a m^3+2 a m=0 i

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Paragraph: Read the following write up carefully and answer the following questions: Consider a parabola, y ^2=4 ax then y + tx = at ^3+2 at represents a normal at a point (at ^2, 2 a t ). It can also be represented as y-m x+a m^3+2 a m=0 in its slope form. Considering the above equation and assuming it passes through a point P(h, k) we can say that k-m h+a m^3+2 a m=0 a m^3+m(2 a-h)+k=0 from P(h, k) maximum 3 normal

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Correct answer: A. 1

Let P(h, k) be the point a m^3+m(2 a-h)+k=0 Since, m ₁, ~m ₁, ~m ₁ are the possible roots 3 ~m ₁=0 m ₁=0 If m₁=0 is the root then k=0 aligned & am ^3+ m (2 a - h )=0 & m ^2= h -2 a a =0 h =2 a aligned (2 a , 0) is the only point

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