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 PUBLICATION|Exercise EXERCISE (SINGLE CORRECT ANSWER TYPE)|82 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXERCISE (MULTIPLE CORRECT ANSWERS TYPE)|30 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.5|8 Videos

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

Similar Questions

Explore conceptually related problems

Consider the family of lines (x+y-1)+lambda(2x+3y-5)=0 and (3x+2y-4)+ mu(x+2y-6)=0 , equation of a straight line that belongs to both the families is

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 a straight line mid - way between the lines 2x+3y=5and2x+3y+1=0 .

If x^2-3xy+lambda y^2+3x-5y+2=0 ,represent a pair of straight lines, then the value of lambda is

Find the equation of the straight line equidistant from the point (2,-2) and the line 3x-4y+1=0.

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

Find the equation of the line passing through (1,1) and parallel to the line 2x-3y+5=0.

A diagonal of rhombus A B C D is member of both the families of lines (x+y-1)+lambda(2x+3y-2)=0 and (x-y+2)+ lamda(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 lambda x^(2) + 4xy + y^(2) + lambda x + 3y + 2 = 0 represents the equation of the parabola , then the vlaue of lambda is _

Consider the straight lines x+2y+4=0 and 4x+2y-1=0. The line 6x+6y+7=0 is