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JEE Main 202430 JanuaryMorning Shift
Exam
JEE Main
Year
2024
Date
30 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2024 · 30 January · Morning Shift · Mathematics · Straight Lines

A line passing through the point A ( 9, 0 ) makes an angle of 30 °...

A line passing through the point A(9,0)A ( 9, 0 ) makes an angle of 30°30 ° with the positive direction of xx-axis. If this line is rotated about AA through an angle of 15°15 ° in the clockwise direction, then its equation in the new position isA line passing through the point A ( 9, 0 ) makes an angle of 30 ° with the positive direction of x -axis. If this line

Options

  1. Ay3−2+x=9\dfrac{y}{\sqrt{3} - 2} + x = 9
  2. Bx3−2+y=9\dfrac{x}{\sqrt{3} - 2} + y = 9
  3. Cx3+2+y=9\dfrac{x}{\sqrt{3} + 2} + y = 9
  4. Dy3+2+x=9\dfrac{y}{\sqrt{3} + 2} + x = 9

Correct answer

A. y3−2+x=9\dfrac{y}{\sqrt{3} - 2} + x = 9

Step-by-step solution

Given,

A straight line passes through $A(9,0)A\left(9, 0\right) and makes a angle 30° withthe{30}^{°} with thex -axis,</p><p>And itisrotatedbyaxis,</p><p>And it is rotated by{15}^{°}degreeclockwise</p><p>So,thenewanglewiththedegree clockwise</p><p>So, the new angle with thex -axiswillbeaxis will be\theta = {30}^{°} - {15}^{°} = {15}^{°}</p><p><imgalt=""src="https://cdn−question−pool.getmarks.app/pyq/jeemain/16264301−8f71−4f14−8167−bfd7dcc56e80.png"style="width:250px;height:189px;"/></p><p>Hence,theequationofthelinewillbe,</p><p></p><p><img alt="" src="https://cdn-question-pool.Quantrex.app/pyq/jee_main/16264301-8f71-4f14-8167-bfd7dcc56e80.png" style="width: 250px; height: 189px;"/></p><p>Hence, the equation of the line will be,</p><p>y - 0 = tan{15}^{°}\left(x - 9\right)</p><p></p><p>⇒ y = \tan \left({45}^{°} - {30}^{°}\right)\left(x - 9\right)</p><p></p><p>⇒ y = \dfrac{1 - \dfrac{1}{\sqrt{3}}}{1 + \dfrac{1}{\sqrt{3}}}\left(x - 9\right)</p><p></p><p>⇒ y = \left(2 - \sqrt{3}\right)\left(x - 9\right)$

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