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JEE Main 20245 AprilEvening Shift

Exam: JEE Main
Year: 2024
Date: 5 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Straight Lines

JEE Main 2024 · 5 April · Evening Shift · Mathematics · Straight Lines

Let A(-1,1) and B(2,3) be two points and P be a variable point...

Let

A(-1,1)

and

B(2,3)

be two points and

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{a} x+\mathrm{b} y=15

, then

5 \mathrm{a}+2 \mathrm{~b}

is :

Let A(-1,1) and B(2,3) be two points and P be a variable point above the line A B such that the area of PAB is 10 . If

Options

A6
B $-\frac{6}{5}$
C4
D $-\frac{12}{5}$

Correct answer

D. $-\frac{12}{5}$

Step-by-step solution

Let A(-1,1) and B(2,3) be two points and P be a variable point above the line A B such that the area of PAB is 10 . If

\begin{aligned} & \frac{1}{2}\left|\begin{array}{ccc}\mathrm{h} & \mathrm{k} & 1 \\ -1 & 1 & 1 \\ 2 & 3 & 1\end{array}\right|=10 \\ & -2 \mathrm{x}+3 \mathrm{y}=25 \\ & -\frac{6}{5} \mathrm{x}+\frac{9}{5} \mathrm{y}=15 \\ & \mathrm{a}=-\frac{6}{5}, \mathrm{~b}=\frac{9}{5} \\ & 5 \mathrm{a}=-6,2 \mathrm{~b}=\frac{18}{5}\end{aligned}

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