If one of the lines represented by ax^2+2hxy+by^2=0 is the Y-axis, then what is the equation of the other line?
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ax
2
+2hxy+by
2
=0⟶ (i)y−m
1
x=0
(ii)y−m
2
x=0
Taking conman of x
2
.
x
2
by
2
+
x
2hy
=0⟶ (i)m
1
(ii)m
2
m
1
+m
2
=−
b
2h
m
1
m
2
=
b
a
Given line px+qy=0
m=
q
−p
Let's say m
1
⊥m
m
1
.m=−1
m
1
×
q
−p
=−1
m
1
=
p
q
Putting the value of slope in eq (i)
b.
p
2
q
2
+2h.
p
q
+a=0
bq
2
+2hpq+ap
2
=0
(Hence
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