QJEEM23Ma5944: JEE Main 2023 Mathematics - Class 11 JEEM23Ma5944 Solution: The equations of the sides AB, BC and CA of a triangle ABC are…

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QJEEM23Ma5944: JEE Main 2023 Mathematics - Class 11 JEEM23Ma5944 Solution: The equations of the sides AB, BC and CA of a triangle ABC are…

The equations of the sides AB, BC and CA of a triangle ABC are : $2 x + y = 0, x + p y = 21 a, (a \pm 0)$ and $x - y = 3$ respectively. Let P(2, a) be the centroid of $Δ$ ABC. Then (BC) $^{2}$ is equal to ___________.

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Accepted Answer

JEE Main 2023 (Online) 24th January Evening Shift Mathematics - Straight Lines and Pair of Straight Lines Question 41 English Explanation

∵ \frac{21 a}{1 - 2 p} + 1 + \frac{3 p + 21 a}{p + 1} = 6

\begin{aligned} ∴ 4 p^{2} - 21 a p + 8 p + 42 a - 5 = 0 . . . (1) \end{aligned}

And

\frac{-42 a}{1-2 p}-2+\frac{21 a-3}{p+1}=3 a

∴ 4 p^{2} - 81 a p + 6 a p^{2} - 24 a + 8 p - 5 = 0 . . . (2)

From equation (1) - equation (2) we get;

60 a p + 66 a - 6 a p^{2} = 0

\begin{array}{r} ∵ a \neq 0 \Rightarrow p^{2} - 10 p - 11 = 0 \\ p = - 1 or 11 \Rightarrow p = 11 . \end{array}

When

p=11

then

a=3

Coordinate of

B=(-3,6)

And coordinate of

C=(8,5)

\therefore B C^{2}=122

QJEEM23Ma5944: JEE Main 2023 Mathematics - Class 11 JEEM23Ma5944 Solution: The equations of the sides AB, BC and CA of a triangle ABC are…

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