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QJEEM16Mab958: JEE Main 2016 Mathematics - Class 11 JEEM16Mab958 Solution: A ray of light is incident along a line which meets another…

A ray of light is incident along a line which meets another line, 7x − y + 1 = 0, at the point (0, 1). The ray is then reflected from this point along the line, y + 2x = 1. Then the equation of the line of incidence of the ray of light is :

Multiple Choice Options

  • A 41x − 38y + 38 = 0
  • B 41x + 25y − 25 = 0
  • C 41x + 38y − 38 = 0
  • D 41x − 25y + 25 = 0

Step-by-Step Verified Solution

Let slope of incident ray be m.

∴\therefore    angle of incidence = angle of reflection

JEE Main 2016 (Online) 10th April Morning Slot Mathematics - Straight Lines and Pair of Straight Lines Question 116 English Explanation

∴\therefore     ∣m−71+7m∣=∣−2−71−14∣=913\left| {{{m - 7} \over {1 + 7m}}} \right| = \left| {{{ - 2 - 7} \over {1 - 14}}} \right| = {9 \over {13}}

⇒\Rightarrow     m−71+7m=913{{m - 7} \over {1 + 7m}} = {9 \over {13}}

  or   m−71+7m=−913{{m - 7} \over {1 + 7m}} = - {9 \over {13}}

⇒\Rightarrow    13m −- 91 == 9 + 63m

   or   13m −- 91 == −- 9 −- 63m

⇒\Rightarrow    50m == −- 100  or  76m == 82

⇒\Rightarrow    m == −12- {1 \over 2}

  or  m == 4138{{41} \over {38}}

⇒\Rightarrow    y −- 1 == −- 12{1 \over 2} (x −- 0)

  or   y −- 1 == 4138{{41} \over {38}} (x −- 0)

i.e   x + 2y −- 2 == 0

  or   38y −- 38 −- 41x == 0

⇒\Rightarrow    41x −- 38y + 38 == 0

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