JEE Main 2022 · 25 Jul · Shift 1 · Mathematics Q12

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MathematicsSingle correct+4 / -1Question 12 of 90

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 $\dfrac{\sqrt{29}}3$ , then B also lies on the line :

2x+y=9

3x-2y=7

x+2y=6

2x-3y=3

Answer and worked solution

Official answer: C

B $=(t,t-2)$ : $(t-4)^2+(t-5)^2=\frac{29}9$ gives $t=\frac{17}3$ or $\frac{10}3$ ; slope above 1 needs $t=\frac{10}3$ , $B=\left(\frac{10}3,\frac43\right)$ .

Check. $x+2y=6$ .

(C)

Topics:Distance and section formulae Equations of a line

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JEE Main 2022 · 25 Jul · Shift 1, Mathematics question 12