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Hyperbola
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Section:
Mathematics
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© examsnet.com
Question : 12 of 92
Marks:
+1
,
-0
If the equation of the hyperbola with foci
(
4
,
2
)
and
(
8
,
2
)
is
3
x
2
−
y
2
−
α
x
+
β
y
+
γ
=
0
, then
α
+
β
+
γ
is equal to
_
_
_
_
.
[3 Apr 2025 Shift 2]
Your Answer:
Validate
Solution:
Given
(
x
−
6
)
2
a
2
−
(
y
−
2
)
2
b
2
=
1
⇒
b
2
x
2
−
a
2
y
2
−
12
x
b
2
+
4
y
a
2
+
36
b
2
−
4
a
2
−
a
2
b
2
=
0
Comparing
b
2
a
2
=
3
⇒
e
2
=
1
+
b
2
a
2
⇒
e
2
=
4
⇒
e
=
2
Similarly, 2ae
=
4
⇒
a
=
1
⇒
b
=
√
3
(
x
−
6
)
2
1
−
(
y
−
2
)
2
3
=
1
⇒
3
x
2
−
y
2
−
36
x
+
4
y
+
108
−
4
−
3
=
0
⇒
3
x
2
−
y
2
−
36
x
+
4
y
+
101
=
0
⇒
α
=
36
,
β
=
4
,
γ
=
101
⇒
α
+
β
+
γ
=
141
© examsnet.com
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