JEE Main 2022 · 29 Jul · Shift 1 · Mathematics Q13

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MathematicsSingle correct+4 / -1Question 13 of 90

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(k $_1$ , k $_2$ ), then k $_1$ + k $_2$ is equal to :

\dfrac47

\dfrac27

Answer and worked solution

Official answer: B

Equal distances. $PA=PC$ gives $(b-1)^2=4$ ; $PB^2=20=PA^2$ gives $(a-1)^2=16$ . With $ab>0$ and A ≠ C: $a=-3$ , $b=-1$ .

Lines. AP: $x+2y=3$ ; BC through $(-1,5)$ , $(-3,-1)$ : $y=3x+8$ . They meet at $\left(-\frac{13}7,\frac{17}7\right)$ ; sum $\frac47$ .

(B)

Topics:Equations of a line Equation of a circle

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JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 13