Maths-
General
Easy

Question

# If the equation  represents a pair of straight lines then their point of intersection is

Hint:

## The correct answer is: (-3, -1)

### Given That:If the equation  represents a pair of straight lines then their point of intersection is>>> λx2 – 5xy + 6y2 + x – 3y = 0>>> Comparing with general equation, ax2 + 2hxy + by2 + 2gx + 2fy + c = 0We get a = λ, h = -5/2, b = 6, g = 1/2, f = -3/2, c = 0>>> The condition for straight lines is abc + 2fgh – af2 – bg2 – ch2 = 0=> λ×6×0 + 2×-3/2×1/2×-5/2 – λ×9/4 – 6×1/4 – 0 = 0=> 0 + 15/4 – 9λ/4 – 3/2 = 0=> 9/4 = 9λ/4=> λ = 1>>>> So the equation becomes x2 – 5xy + 6y2 + x – 3y = 0=> x2 – 3xy – 2xy + 6y2 + x – 3y = 0=> x(x – 3y) – 2y(x – 3y) + x – 3y =0=> (x – 3y)(x – 2y + 1) = 0So x – 3y = 0 …(i)x – 2y + 1 = 0 ..(ii)Solving (i) and (ii)We get x = -3, y = -1>>>The point of intersection of the pair of straight lines x2 – 5xy + 6y2 + x – 3y = 0 is (-3, -1)

>>>The point of intersection of the pair of straight lines x2 – 5xy + 6y2 + x – 3y = 0 is (-3, -1)