Home
Class 12
MATHS
Consider the family of lines 5x+3y-2+lam...

Consider the family of lines `5x+3y-2+lambda_(1)(3x-y-4)=0 " and " x-y+1+lambda_(2)(2x-y-2)=0`. Find the equation of a straight line that belongs to both the families.

Text Solution

Verified by Experts

`"Lines" 5x+3y-2+lambda_(1)(3x-y-4) = 0 " are concurrent at" (1,-1) " and lines" x-y+1+lambda_(2)(2x-y-2) = 0` are concurrent at (3,4).
Thus, the equation of line common to both familes is
`y-4 = (-1-4)/(1-3)(x-3)`
i.e., 5x-2y-7=0
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise (Single)|82 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise (Multiple)|30 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise 2.5|8 Videos

  • STRAIGHT LINE

    CENGAGE|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise JEE Advanced Previous Year|9 Videos

Similar Questions

Explore conceptually related problems

Consider a family of straight lines (x+y)+lambda(2x-y+1)=0 . Find the equation of the straight line belonging to this family that is farthest from (1,-3)dot

Find the equation of the family of circles touching the lines x^2-y^2+2y-1=0.

A diagonal of rhombus A B C D is member of both the families of lines (x+y-1)+lambda1(2x+3y-2)=0 and (x-y+2)+lambda2(2x-3y+5)=0 and rhombus is (3, 2). If the area of the rhombus is 12sqrt(5) sq. units, then find the remaining vertices of the rhombus.

If lambdax^(2)-10xy+12y^(2)+5x-16y-3=0 , represents a pair of straight lines, then the value of lambda is

The equation of straight line belonging to both the families of lines (x-y+1)+lambda_1(2x-y-2)=0 and (5x+3y-2)+lambda_2(3x-y-4)=0 where lambda_1, lambda_2 are arbitrary numbers is (A) 5x -2y -7=0 (B) 2x+ 5y - 7= 0 (C) 5x + 2y -7 =0 (D) 2x- 5y- 7= 0

Find the equation of the bisectors of the anglebetween the lines 4x+3y=5 and x +2y+3=0.

If the equation of any two diagonals of a regular pentagon belongs to the family of lines (1+2lambda)y-(2+lambda)x+1-lambda=0 and their lengths are sin 36^0 , then the locus of the center of circle circumscribing the given pentagon (the triangles formed by these diagonals with the sides of pentagon have no side common) is (a) x^2+y^2-2x-2y+1+sin^2 72^0=0 (b) x^2+y^2-2x-2y+cos^2 72^0=0 (c) x^2+y^2-2x-2y+1+cos^2 72^0=0 (d) x^2+y^2-2x-2y+sin^2 72^0=0

Consider the lines given by L_(1):x+3y-5=0 L_(2):3x-ky-1=0 L_(3):5x+2y-12=0 Match the following lists.