(5) Find the condition that the line 3x + y = 0 may be perpendicular to one + of the lines given by ax2 +2hxy +by2=0.
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Answer:
The line 3x+y=0 may be perpendicular to one of the line given by ax
2
+2hxy+by
2
=0
Auxiliary equation=bm
2
+2hm+a=0⟶(1)
3x+y=0
slope(m
1
)=−3
Hence slope of the line perpendicular to given line.
∴ Slope of one of the lines represented by the joint equation is
3
1
.
Now
3
1
must be one of the roots of equation
b(
3
1
)
2
+2h(
3
1
)+a=0
b
9
1
+
3
2h
+0
b+6h+9a=0(The required condition)
Step-by-step explanation:
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