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Byju's Answer
Standard XII
Mathematics
Homogenization
If a pair of ...
Question
If a pair of lines
x
2
−
2
p
x
y
−
y
2
=
0
and
x
2
−
2
p
x
y
−
y
2
=
0
is such that each pair bisects the angle between the other pair, prove that
p
q
=
−
1
.
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Solution
Equations of the bisectors of
x
2
−
2
p
x
y
−
y
2
=
0
are
x
2
−
y
2
1
−
(
−
1
)
=
x
y
−
p
or
x
2
−
y
2
=
−
2
x
y
p
..
(
1
)
But the bisectors of first pair of lines are given by the
2
nd paid, i.e., by
x
2
−
y
2
=
2
q
x
y
..
(
2
)
Comparing
(
1
)
and
(
2
)
, we get
−
1
/
p
=
q
or
p
q
=
1
or
p
q
+
1
=
0
.
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0
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