show that the lines x24xy+y2=0 and x+y=3 form an equilateral triangle also find area of the triangle
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1. User Answers Anonym
Given pair of lines are x² + 4xy + y² = 0
⇒ (y/x) ² + 4 y/x + 1 = 0
⇒ y/x = 4±2√3/2 = 2±√3,
∴ The lines y = (2 + √3) x and y = (2  √3) x and x  y = 4 forms an equilateral triangle
Clearly the pair of lines x² + 4xy +y² = 0 intersect at origin,
The perpendicular distance form origin to x  y = 4 is the height of the
h = 2 √ 2
∵ Area of triangle = h²/√3 = 8/√3