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QJEEM22Mae089: JEE Main 2022 Mathematics - Class 11 JEEM22Mae089 Solution: Let the circumcentre of a triangle with vertices A(a, 3), B(b,…

Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1,1). If the line AP intersects the line BC at the point Q (k1,k2)\left(k_{1}, k_{2}\right) , then k1+k2k_{1}+k_{2} is equal to :

Multiple Choice Options

  • A 2
  • B 47\frac{4}{7}
  • C 27\frac{2}{7}
  • D 4

Step-by-Step Verified Solution

JEE Main 2022 (Online) 29th July Morning Shift Mathematics - Straight Lines and Pair of Straight Lines Question 48 English Explanation

Let D be mid-point of AC, then

b+32=1⇒b=−1{{b + 3} \over 2} = 1 \Rightarrow b = - 1

Let E be mid-point of BC,

5−bb−a . (3+b)2a+b2−1=−1{{5 - b} \over {b - a}}\,.\,{{{{(3 + b)} \over 2}} \over {{{a + b} \over 2} - 1}} = - 1

On putting b=−1b = - 1 , we get a=5a = 5 or −3-3

But a=5a = 5 is rejected as ab > 0

A(−3,3), B(−1,5), C(−3,−1), P(1,1)A( - 3,3),\,B( - 1,5),\,C( - 3, - 1),\,P(1,1)

Line BC⇒y=3x+8BC \Rightarrow y = 3x + 8

Line AP⇒y=3−x2AP \Rightarrow y = {{3 - x} \over 2}

Point of intersection (−137,177)\left( {{{ - 13} \over 7},{{17} \over 7}} \right)

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