NTA Abhyas JEE Main2020MathematicsParabolaPractice

The shortest distance of 0,3 from the parabola y = x 2 is

Options

A3 units
B11 2 units
C10 2 units
D5 2 units

Correct answer

B. 11 2 units

Step-by-step solution

Any point on the parabola is x , x 2 Distance between ( x , x 2 ) and ( 0,3 ) is D = x 2 + x 2 - 3 2 D 2 = x 2 - 5 2 2 + 3 - 1 4 is minimum if x 2 - 5 2 = 0 Hence, D m i n = 11 4 = 11 2 units

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