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KEAM 2017 Math Paper
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© examsnet.com
Question : 22
Total: 120
The equation of the hyperbola with vertices (0,±15) and foci (0,± 20) is
x
2
175
−
y
2
225
=
1
x
2
625
−
y
2
125
=
1
x
2
225
−
y
2
125
=
1
x
2
65
−
y
2
65
=
1
x
2
225
−
y
2
175
=
1
Validate
Solution:
We have
Vertices and foci of hyperbola at
(
0
,
±
15
)
and
(
0
,
±
20
)
since, both foci and vertices lies on
Y
-axis, then equation of hyperbola will be
y
2
b
2
−
x
2
a
2
=
1
Now, vertices
=
(
0
,
±
b
)
∴
b
=
15
Again, foci
=
(
0
,
±
b
e
)
∴
b
e
=
20
⇒
e
=
20
15
=
4
3
⇒
√
1
+
a
2
b
2
=
4
3
[
∵
e
=
√
1
+
a
2
b
2
]
⇒
1
+
a
2
b
2
=
16
9
⇒
a
2
b
2
=
7
9
⇒
a
2
=
7
9
×
b
2
=
7
9
×
225
⇒
a
=
√
7
3
×
15
=
5
√
7
∴
Equation of hyperbola is
y
2
225
−
x
2
175
=
1
© examsnet.com
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