Straight Line and Pair of Straight Lines 1 Question 5

5. If the two lines x+(a1)y=1 and 2x+a2y=1,(aR0,1) are perpendicular, then the distance of their point of intersection from the origin is

(a) 25

(b) 25

(c) 25

(d) 25

(2019 Main, 9 April II)

Show Answer

Solution:

Key Idea

(i) If lines are perpendicular to each other, then product of their slopes is -1 , i.e. m1m2=1

(ii) Distance between two points (x1,y1) and (x2,y2)

=(x2x1)2+(y2y1)2

Given, lines x+(a1)y=1

and 2x+a2y=1, where aR0,1

are perpendicular to each other

1a1×2a2=1

[ If lines are perpendicular, then product of their slopes is -1 ]

a2(a1)=2a3a2+2=0

(a+1)(a22a+2)=0a=1

Equation of lines are

x2y=1

and 2x+y=1

On solving Eq. (i) and Eq. (ii), we get

x=35 and y=15

Point of intersection of the lines (i) and (ii) is P35,15.

Now, required distance of the point P35,15 from origin =925+125=1025=25



NCERT Chapter Video Solution

Dual Pane