Question

Find straight lines represented by 6x2 + 13xy + 6y2 + 8x + 7y + 2 = 0 and also find the point of intersection.  

Solution

Correct option is

         

         

                                                                          

Identically. Hence given equation represents a pair of lines.

To find the lines, we rewrite the given equation as

6x2 + (13y + 8)x + (6y2 + 7y + 2) = 0,  

(a quadratic in x)

Solve for x:  

         

      

Hence lines are 3x + 2y + 1 = 0                           … (i)

2x + 3y + 2 = 0                                                     … (ii)

Solve eqs. (i) & (ii) for the point of intersection, we get

  

Thus lines intersect at point

SIMILAR QUESTIONS

Q1

Find the equation of a line parallel to x + 2y = 3 and passing through the point (3, 4).

Q2

Find the equation of the line perpendicular to 2x – 3y = 5 and cutting off an intercept 1 on the x-axis

Q3

Find the equation of the straight line passing through (2, –9) and the point of intersection of lines 2x + 5y – 8 = 0,

3x – 4y – 35 = 0  

Q4

Find the equation of straight line passing through the point of intersection of lines 3x – 4y +1 = 0, 5x + y – 1 = 0 and cutting off equal intercepts from coordinate axes.

Q5

Find the distance between the lines 5x + 12y + 40 = 0 and 10x + 24y – 25 = 0.

 

Q6

If P is (1, 2) and the line mirror is 2x – y + 4 = 0, find the coordinates of its image (i.e., Q).

Q7

Find the values of λ for which the point (2 – λ, 1 + 2λ) lies on the non-origin side of the line 4x – y – 2 = 0. 

Q8

Find the incentre of ΔABC if A is (4, –2), B is (–2, 4) and C is (5, 5).

Q9

Find the coordinates of the orthcentre of the triangle whose vertices are (0, 0), (2, –1) and (–1, 3).

Q10

If abc are all distinct, then the equations (b – c)x + (c – a)y + a – b = 0 and (b3 – c3)x + (c3 – a3)y + a3 – b3 = 0 represent the same line if