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JEE Main 20199 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
9 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Parabola

JEE Main 2019 · 9 January · Morning Shift · Mathematics · Parabola

Axis of a parabola lies along x -axis. If its vertex and focus are...

Axis of a parabola lies along xx-axis. If its vertex and focus are at distances 22 and 44 respectively from the origin, on the positive xx-axis then which of following points does not lie on it?Axis of a parabola lies along x -axis. If its vertex and focus are at distances 2 and 4 respectively from the origin,

Options

  1. A(6,42)\left(6, 4\sqrt{2}\right)
  2. B(5,26)\left(5, 2\sqrt{6}\right)
  3. C(8,6)\left(8, 6\right)
  4. D(4,−4)\left(4, - 4\right)

Correct answer

C. (8,6)\left(8, 6\right)

Step-by-step solution

Axis of a parabola lies along x -axis. If its vertex and focus are at distances 2 and 4 respectively from the origin,
Clearly vertex is (2,0)\left(2, 0\right) and focus is S(4,0)⇒a=2S\left(4, 0\right) ⇒ a = 2 .

Hence, the equation of parabola is y2=4×2(x−2){y}^{2} = 4 \times 2\left(x - 2\right)

⇒y2=8(x−2)</p><p>⇒ {y}^{2} = 8 \left(x - 2\right)</p><p>⇒Point(8,6)doesnotlieonPoint \left(8, 6\right) does not lie on the parabola.

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