A line, with the slope greater than one, passes through the point A (4,3) and intersects the line x-y-2=0 at the point B. If the length of the line segment AB is (√29/3), then B also lies on the line :

Question

A line, with the slope greater than one, passes through the point A (4,3) and intersects the line x-y-2=0 at the point B. If the length of the line segment AB is (√29/3), then B also lies on the line : (A) 2 x+y=9 (B) 3 x-2 y=7 (C) x+2 y=6 (D) 2 x -3 y =3

Tardigrade Admin · Accepted Answer

Let B(x1, x1-2) √(x1-4)2+(x1-2-3)2=(√29/3) Squaring on both side 18 x 12-162 x 1+340=0 x 1=(51/9) or x 1=(10/3) y 1=(33/9) or y 1=(4/3) Option (C) will satisfy ((10/3), (4/3))

Q. A line, with the slope greater than one, passes through the point $A (4, 3)$ and intersects the line $x - y - 2 = 0$ at the point $B$ . If the length of the line segment $A B$ is $\frac{29}{3}$ , then $B$ also lies on the line :

$2 x + y = 9$

$3 x - 2 y = 7$

$x + 2 y = 6$

$2 x - 3 y = 3$

Let $B (x_{1}, x_{1} - 2)$
$(x_{1} - 4)^{2} + (x_{1} - 2 - 3)^{2} = \frac{29}{3}$
Squaring on both side $18 x_{1}^{2} - 162 x_{1} + 340 = 0$
$x_{1} = \frac{51}{9}$ or $x_{1} = \frac{10}{3}$
$y_{1} = \frac{33}{9}$ or $y_{1} = \frac{4}{3}$
Option (C) will satisfy $(\frac{10}{3}, \frac{4}{3})$

Q. A line, with the slope greater than one, passes through the point A(4,3) and intersects the line x−y−2=0 at the point B. If the length of the line segment AB is 329​​, then B also lies on the line :

2x+y=9

3x−2y=7

x+2y=6

2x−3y=3