Mathematics · Straight lines

JEE Main 2024 — 31 January, Shift 2 — Question 2

Let $\mathrm{A}(\mathrm{a}, \mathrm{b}), \mathrm{B}(3,4)$ and $(-6,-8)$ respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point $P(2 a+3,7 b+5)$ from the line $2 x+3 y-4=0$ measured parallel to the line $x-2 y-1=0$ is

Option A:
$\frac{15 \sqrt{5}}{7}$
Option B:
$\frac{17 \sqrt{5}}{6}$
Option C:
$\frac{17 \sqrt{5}}{7}$
Correct
Option D:
$\frac{\sqrt{5}}{17}$

Answer: C

Step-by-step solution

$\mathrm{A}(\mathrm{a}, \mathrm{b}), \mathrm{B}(3,4), \quad \mathrm{C}(-6,-8)$

$\Rightarrow \mathrm{a}=0,\mathrm{~b}=0 \quad \Rightarrow \mathrm{P}(3,5)$

Distance from P measured along $\mathrm{x}-2 \mathrm{y}-1=0$

$\Rightarrow x=3+r \cos \theta, \quad y=5+r \sin \theta$

Where $\tan \theta=\frac{1}{2}$

$r(2 \cos \theta+3 \sin \theta)=-17$

$\Rightarrow \mathrm{r}=\left|\frac{-17 \sqrt{5}}{7}\right|=\frac{17 \sqrt{5}}{7}$

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Exam: JEE Main 2024
Paper: 31 January, Shift 2
Subject: Mathematics
Chapter: Straight lines
Topic: Various forms of lines

Let A(-2,-1), B(1,0), C(alpha, beta) and D(gamma, delta) be the vertices of a parallelogram ABCD . If the point C lies on 2 x- y=5 and the…

Answer: C

Step-by-step solution

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