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JEE Main202229 Jul 2022Morning ShiftMathematicsStraight LinesActual

Let the circumcentre of a triangle with vertices A a , 3 , B b , 5 and C a , b , a b > 0 be P 1 , 1 . If the line A P intersects the line B C at the point Q k 1 , k 2 , then k 1 + k 2 is equal to

Options

  1. A2
  2. B4 7
  3. C2 7
  4. D4

Correct answer

B. 4 7

Step-by-step solution

On plotting the graph we get, Now by diagram m A C ⟶ ∞ and m P D = 0 as P D is perpendicular bisector, so D a + a 2 , b + 3 2 ≡ D a , b + 3 2 Now since m P D = 0 , so b + 3 2 - 1 = 0 ⇒ b + 3 - 2 = 0 ⇒ b = - 1 Now similarly finding the coordinates of E b + a 2 , 5 + b 2 = a - 1 2 , 2   as   b = - 1 Now we know that product of perpendicular slopes is m C B · m E P = - 1 ⇒ 5 - b b - a = 2 - 1 a - 1 2 - 1 = - 1 ⇒ 6 - 1 - a = 2 a - 3 = - 1 ⇒ 12 = 1 + a a -

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