find the value of sum of the slopes for pairs of lines x2+8xy+y2is equal to 0
Answers
Answer:
k=-2
Step-by-step explanation:
Let the lines represented by the equation.
x
2
+kxy−3y
2
=0
⇒ −
3
x
2
−
3
k
xy+y
2
=0 be y=m
1
x and y=m
2
x, where m
1
and m
2
are the slopes of the lines.
⇒ −
3
x
2
−
3
k
xy+y
2
=(y−m
1
x)(y−m
2
x)
⇒ −
3
x
2
−
3
k
xy+y
2
=y
2
−(m
1
+m
2
)xy+(m
1
m
2
)x
2
Comparing both sides, we get
C(m
1
+m
2
)=
3
k
and (m
1
m
2
)=−
3
1
Given, m
1
+m
2
=2m
1
m
2
∴
3
k
=2(−
3
1
)
∴k=−2
Given : Equation of Pair of lines x² + 8xy + y² = 0
To Find : sum of the slopes of the lines
Solution:
x² + 8xy + y² = 0
=> y² + 8xy + x² = 0
Sum of slopes of the lines = - 8
Product of slopes = 1
value of sum of the slopes for pairs of lines x² + 8xy + y² = 0 is - 8
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