Home
Class 12
MATHS
If the two lines x+(a-1)=1 and 2x+a^(2)y...

If the two lines x+(a-1)=1 and `2x+a^(2)y=1(ainR-{0,1)}` are perpendicular, then the distance of their point of intersection from the origin is :

A

`(2)/(sqrt(5))`

B

`(sqrt(2))/(5)`

C

`sqrt((2)/(5))`

D

`(2)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
C
x + (a - 1) y = 1
`2x + a^(2) y = 1` `a in R - {0, 1}`, `m_(1) m_(2) = - 1`
`- (1)/(a - 1). (-2)/(a^(2)) = - 1` `-2 = a^(3) - a^(2)` , `a^(3) - a^(2) + 2 = 0 implies` a = - 1
`:.` lines are x - 2y = 1 and 2x + y = 1 `:.` point of intersection of lines is `((3)/(5), - (1)/(5))`
Distance from origin `= sqrt((9)/(25) + (1)/(25)) = sqrt((10)/(25)) = sqrt((2)/(5))`
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISION TEST 11 (2020)

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION - 2)|4 Videos

  • JEE MAIN REVISION TEST -17 (2020)

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

  • JEE MAIN REVISION TEST 5 (2020)

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

If the lines x+(a-1)y=1 and 2x+1a^(2)y=1 there ainR-{0,1} are perpendicular to each other, Then distance of their point of intersection from the origin is

If the lines x+(a-1)y+1=0 and 2x+a^2y-1=0 are perpendicular, then find the value of adot

The perpendicular distance from the point (1,-1) to the line x+5y-9=0 is equal to

Show that the two lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-4)/5=(y-1)/2=z intersect. Find also the point of intersection of these lines.

Find the perpendicular distance of the point (1, 1, 1) from the line (x-2)/(2)=(y+3)/(2)=(z)/(-1) .

Find the perpendicular distasnce of the point (1,0,0) from the lines (x-1)/2=(y+1)/(-3)=(z+10)/8

Find the equation of the plane through the line of intersection of the planes x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z=0 . Then find the distance of plane thus obtained from the point A(1,3,6) .

If a certain line intersects the origin and is perpendicular to the line with the equation y = 2x+5 at point P, what is the distance from the origin to point P ?

If plane passes through the point (1, 1,1) and is perpendicular to the line, (x-1)/3=(y-1)/0=(z-1)/4 , then its perpendicular distance from the origin is

If plane passes through the point (1, 1,1) and is perpendicular to the line, (x-1)/3=(y-1)/0=(z-1)/4 , then its perpendicular distance from the origin is