If the area of the triangle formed by the
lines 3x² - 2xy - 8y2 = 0 and the line
2x+y-k=0 is 5 sq. units, then k =
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Given pairs of sides of triangle
8x
2
−6xy+y
2
=0 and side 2x+3y=a
From pairs of sides
8x
2
−4xy−2xy+y
2
=0
4x(2x−y)−y(2x−y)=0
4x−y=0---(1) and 2x−y=0----(2) are the two sides of triangle
From eq (1) and (2)
4x−2x=0⇒x=0,y=0
Point A(0,0) and Third sides is 2x+3y=a---(3)
From eq (2) and (3)
2x+6x=a⇒x=
8
a
,y=
4
a
Point B(
8
a
,
4
a
)
from eq (1) and (3)
2x+12x=a⇒x=
14
a
,y=
7
a
Point C(
14
a
,
14
4a
)
Area of triangle =7
2
1
×
4
a
×
14
a
=7
a
2
=7×14×4×2
a=14×2
a=28
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