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Area of triangle formed by x²-4xy+y²=0, x+y=3 is .....

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Answered by nehasonawane989
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Show that the lines x

2

+4xy+y

2

=0 and x−y=4 form an equilateral triangle. Also find the area of the triangle.

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ANSWER

Given pair of lines are x

2

+4xy+y

2

=0

⟹(

x

y

)

2

+4

x

y

+1=0

x

y

=

2

−4±2

3

=−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 x

2

+4xy+y

2

=0 intersect at origin,

The perpendicular distance form origin to x−y=4 is the height of the equilateral triangle

h=2

2

∴ Area of the triangle is

3

h

2

=

3

8

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