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MHT CET202020 Oct 2020Evening ShiftMathematicsStraight LinesActual

If p₁ and p₂ are the lengths of perendiculars from the origin to the lines x +y =5 2 and x cosec +y -5=0 respectively, then p₁²+4 p₂²=

Options

  1. A1 25
  2. B1 5
  3. C25
  4. D5

Correct answer

C. 25

Step-by-step solution

As per condition given, we write aligned p ₁ &= |-5 2 | ² + ² and p₂= |-5| cosec ² + ² p ₁²= 25 ² 2 1 and 4 p ₂² &= 4(25) cosec ² + ² p ₁²+4 p ₂² &=25 ( ² - ² )²+ 100 ( 1 ² )+ 1 ² &=25( - )²( + )²+100 ² ² &=25(1- 2 )(1+ 2 )+25 (4 ² ² ) &=25 (1- 2 + 2 - ² 2 )+25(2 )² &=25 (1- ² 2 )+25( 2 )² &=25 ( ² 2 )+25 ( ² 2 )=25 aligned

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