Home
Class 12
MATHS
Find the lines whose combined equation i...

Find the lines whose combined equation is `6x^2+5x y-4y^2+7x+13 y-3=0`

Text Solution

Verified by Experts

The given equation of pair of straight lines is
`6x^(2)+5xy-4y^(2)+7x+13y-3=0`
or `6x^(2)+(5y+7)x-(4y^(2)-13y+3)=0`
Solving it as a quadratic in x,we get
`x=((5y+7)+-sqrt((5y+7)^(2)+24(4y^(2)-13y+3)))/(12)`
`=(-(5y+7)+-sqrt(121y^(2)-242y+121))/(12)`
`=(-(5y+7)+-11(y-1))/(12)`
`=(6y-18)/(12),(16y+4)/(12)or(y-3)/(2),(-4y+1)/(3)`
The two straight lines are `2x-y++3=0and3x+4y-1=0`.
Promotional Banner

Topper's Solved these Questions

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise 3.1|6 Videos
  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise 3.2|7 Videos
  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos
  • PARABOLA

    CENGAGE|Exercise Question Bank|21 Videos

Similar Questions

Explore conceptually related problems

Find the lines whose combined equation is 6x^(2)+5xy-4y^(2)+7x+13y-3=0

Find the lines whose combined equation is 6x^(2)+5xy-4y^(2)+7x+13y-3=0

Find the lines whose combined equation is 6x^(2)+5xy-4y^(2)+7x+13y-3=0 using the concept of parallel lines through the origin.

Find the equation of component lines whose combined equation is 6x^(2)+5xy-4y^(2)+7x+13y-3=0 without solving for xor y.

The triangle formed by the lines whose combined equation is (y^(2)-4xy-x^(2))(x+y-1)=0 is

Orthocentre of the triangle formed by the lines whose combined equation is (y ^(2) - 6xy -x ^(2)) ( 4x -y +7) =0 is

Separate equations of lines, whose combined equation is 4x^(2)-y^(2)+2x+y=0 are

Find acute and obtuse angle between companent lines whose combined equation is 2x^(2)+5xy+3y^(2)+6x+7y+4=0 .

Three sides of a triangle are represented by lines whose combined equation is (2x+y-4) (xy-4x-2y+8) = 0 , then the equation of its circumcircle will be : (A) x^2 + y^2 - 2x - 4y = 0 (B) x^2 + y^2 + 2x + 4y = 0 (C) x^2 + y^2 - 2x + 4y = 0 (D) x^2 + y^2 + 2x - 4y = 0

If theta is the angle between the lines given by the equation 6x^(2)+5xy-4y^(2)+7x+13y-3=0, then find the equation of the line passing through the point of intersection of these lines and making an angle theta with the positive x -axis.