NTA Abhyas JEE Main2020MathematicsParabolaPractice

The set of points on the axis of the parabola y 2 - 2 y - 4 x + 5 = 0 from which all the three normals drawn to the parabola are real and distinct, is

Options

Ax , 1 : x > 3
Bx , - 1 : x ≥ 1
Cx , 3 : x ≥ 1
Dx , - 3 : x ≥ 3

Correct answer

A. x , 1 : x > 3

Step-by-step solution

Given equation of the parabola can be rewritten as ( y - 1 ) 2 = 4 ( x - 1 ) Axis of the parabola is y = 1 , equation of normal is y - 1 = m x - 1 - 2 m - m 3 Let ( h , 1 ) is a point on its axis, then 0 = m h - 1 - 2 m - m 3 ⇒ m 2 = h - 3 ⇒ h > 3 for real & distinct values of m

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