Let mathrm{A}(-1,1) and mathrm{B}(2,3) be two points and mathrm{P} be a variable point above line A

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3 and 4 .Determinants and Matrices

hard

Let $\mathrm{A}(-1,1)$ and $\mathrm{B}(2,3)$ be two points and $\mathrm{P}$ be a variable point above the line $A B$ such that the area of $\triangle \mathrm{PAB}$ is $10$ . If the locus of $\mathrm{P}$ is $\mathrm{ax}+\mathrm{by}=15$, then $5 a+2 b$ is :

A

$-\frac{12}{5}$

B

$-\frac{6}{5}$

C

$4$

D

$6$

(JEE MAIN-2024)

Solution

$\frac{1}{2}\left|\begin{array}{lll}\mathrm{h} & \mathrm{k} & 1 \\ -1 & 1 & 1 \\ 2 & 3 & 1\end{array}\right|=10$

$ -2 x+3 y=25 $

$ -\frac{6}{5} x+\frac{9}{5} y=15 $

$ a=-\frac{6}{5}, b=\frac{9}{5} $

$ 5 a=-6,2 b=\frac{18}{5}$

Standard 12

Mathematics

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