find the centroid and Area of triangle formed by pair of lines 8x^2-14xy+5y^2=0 and the triangle Straight line x-2y+3=0
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Answer:
12x
2
−20xy+7y
2
=0
Substitute
x
y
=t,
7t
2
−20t+12=0
t=
14
20±
400−336
t=
14
20±8
t=2,
7
6
⇒y=2x ---(1) y=
7
6
x ---(2)
and 3y=2x+4 ---(3)
from 1 & 3, x=1 & y=2
from 2& 3, x=7 & y=6
from 1 & 2, x=0 & y=0
centroid of ΔABC=(
3
x
1
+x
2
+x
3
,
3
y
1
+y
2
+y
3
)
=(
3
8
,
3
8
)
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