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Most Important Selected Qs for JEE AdvancedMathematicsStraight Lines

Let P be any point on the line x-y+3=0 and A be a fixed point (3,4) . If the family of lines given by the equations (3 +5 cosec ) x+(7 -3 cosec ) y+11( - cosec )=0 are concurrent at a point B for all permissible value of , then:

Options

  1. Asum of the abscissa and ordinate of point B is equal to -1 .
  2. Bproduct of the abscissa and ordinate of point B is equal to -2 .
  3. Cmaximum value of |P A-P B| is 2 10 .
  4. Dminimum value of P A+P B is 2 34 .

Correct answer

C. maximum value of |P A-P B| is 2 10 .

Step-by-step solution

(3 +5 cosec ) x+(7 -3 cosec ) y+11( - cosec )=0 (3 x+7 y+11)+ cosec (5 x-3 y-11)=0 Hence, family of lines are concurrent at the point of intersection of 3 x+7 y+11=0 and 5 x-3 y-11=0 Hence point B is (1,-2) . Now proceed.

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