Home
Class 12
MATHS
The line joining the points A(2,1), and ...

The line joining the points `A(2,1)`, and `B(3,2)` is perpendicular to the line `(a^2)x+(a+2)y+2=0`. Find the values of a.

Text Solution

Verified by Experts

The correct Answer is:
`a=2,-1`
The slope of the line joining `A(2,1) and B(3,2)` is `(2-1)/(3-2)=1`
The slope of the line `(a^2)x+2)y+2=0` is `(a^2)/(a+2)`
The lines are perpendicular. Therefore, `((a^2)/(a+2))(1)=-1`
or `a^2=a+2`
or `a^2-a-2=0`
or `(a-2)(a+1)=0`
or `a=2,-1`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.5|5 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.6|9 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.3|10 Videos

  • COORDINATE SYSTEM

    CENGAGE|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

The line joining the points A(2,1),a n dB(3,2) is perpendicular to the line (a^2)x+(a+2)y+2=0. Find the values of adot

A line passing through the points (a, 2a) and (-2, 3) is perpendicular to the line 4x + 3y + 5 = 0. Find the value of a?

If the line joining the points (6,-2) and (8,4) is perpendicular to the line joining the points (12,8) and (24,y) , find the value of y .

The line joining the points (2, x) and (3, 1) is perpendicular to the line joining the points (x, 4) and (7, 5). The value of x is

A line passing through the points (a, 2a) and (-2, 3) is perpendicular to the line 4x+3y+5=0 , find the value of a .

A line passing through the points (a ,\ 2a) and (-2,\ 3) is perpendicular to the line 4x+3y+5=0 , find the value of adot

If the line joining the points A(2,3,-1) and B(3,5,-3) is perpendicular to the line joining the points C(1,2,3) and D(3,y,7) then y=

Show that the line joining the point A(1,-1,2) and B(3, 4, -2) is perpendicular to the line joining the points C(0,3,2) and D(3,5,6).

if the straight line joining the points (3,4) and (2,-1) be parallel to the line joining the points (a,-2) and (4,-a), find the value of a.

Determine the value of k so that the line joining points A(k,1,-1) and B(2,0,2k) is perpendicular to the line joining the points C(4,2k,1) and D(2,3,2) .