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Byju's Answer
Standard XII
Mathematics
Normal
Find the slop...
Question
Find the slope of common tangent if any to hyperbola
x
2
a
2
−
y
2
b
2
=
1
and
y
2
a
2
−
x
2
b
2
=
1
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Solution
Let tangent line of both hyperbola should be
y
=
x
+
t
,
y
=
x
−
t
,
y
=
−
x
+
t
,
y
=
−
x
−
t
Assume, that line
y
=
(
x
+
t
)
tangent to hyperbola
x
2
a
2
−
y
2
b
2
=
1
,
x
2
a
2
−
(
x
+
t
)
2
b
2
=
1
⇒
x
2
a
2
−
x
2
b
2
−
2
x
t
b
2
−
t
2
b
2
−
1
=
0
⇒
x
2
(
b
2
−
a
2
)
−
2
a
2
x
t
−
a
2
t
2
−
a
2
b
2
=
0
by solving this quadratic equation we get
⇒
t
=
+
√
a
2
−
b
2
o
r
t
=
−
√
a
2
−
b
2
,
t
h
e
n
,
y
=
n
+
√
a
2
−
b
2
⇒
y
=
x
−
√
a
2
−
b
2
,
y
=
−
x
+
√
a
2
−
b
2
,
y
=
−
x
−
√
a
2
−
b
2
,
s
l
o
p
e
=
(
1
,
−
1
)
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0
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