If the three normals drawn to the parabola, y 2 = 2 x pass through the point a , 0 , a ≠ 0 , then a must be greater than :

Question

If the three normals drawn to the parabola, y 2 = 2 x pass through the point a , 0 , a ≠ 0 , then a must be greater than :, 1 2, - 1 2, - 1, 1

MARKS App · Accepted Answer

Let the equation of the normal be y = m x - 2 a m - a m 3 Here 4 a = 2 a = 1 2 y = m x - m - 1 2 m 3 It passes through A ( a , 0 ) then 0 = a m - m - 1 2 m 3 m = 0 , m 2 - 2 ( a - 1 ) = 0 For real values of m 2 ( a - 1 ) > 0 ⇒ a > 1

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