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JEE Main 202125 FebruaryMorning Shift
Exam
JEE Main
Year
2021
Date
25 February
Shift
Morning Shift
Subject
Mathematics
Chapter
Parabola

JEE Main 2021 · 25 February · Morning Shift · Mathematics · Parabola

A tangent is drawn to the parabola y ^ 2 = 6x which is...

A tangent is drawn to the parabola y2=6x{y}^{2} = 6x which is perpendicular to the line 2x+y=12x + y = 1. Which of the following points does NOT lie on it?

Options

  1. A(0,3)\left(0, 3\right)
  2. B(4,5)\left(4, 5\right)
  3. C(5,4)\left(5, 4\right)
  4. D(−6,0)\left(- 6, 0\right)

Correct answer

C. (5,4)\left(5, 4\right)

Step-by-step solution

Slope of tangent =mT=m= {m}_{T} = m

So, m(−2)=−1⇒m=12m\left(- 2\right) = - 1 ⇒ m = \dfrac{1}{2}

Equation: y=mx+amy = mx + \dfrac{a}{m}

⇒y=12x+32×12(∵a=64=32)⇒ y = \dfrac{1}{2}x + \dfrac{3}{2 \times \dfrac{1}{2}}\left(∵ a = \dfrac{6}{4} = \dfrac{3}{2}\right)

⇒y=x2+3⇒ y = \dfrac{x}{2} + 3

⇒2y=x+6⇒ 2y = x + 6

Point \left(5, 4\right) will not lie on it

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