Find the coordinates of the foci and the vertices, the
eccentricity and the length of the latus rectum of the hyperbolas.
Answers
Answer:
The given equation is 5y
2
−9x
2
=36
⇒
(
5
36
)
y
2
−
4
x
2
=1
⇒
(
5
6
)
2
y
2
−
2
2
x
2
=1...(1)
On comparing equation (1) with the standard equation of hyperbola
i.e.,
a
2
y
2
−
b
2
x
2
=1,
we obtain a=
5
6
and b=2
We know that a
2
+b
2
=c
2
, where c=ae
∴c
2
=
5
36
+4=
5
56
⇒c=
5
56
=
5
2
14
Therefore, the coordinates of the foci are (0,±
5
2
14
)
The coordinates of the vertices are (0,±
5
6
)
Eccentricity e=
a
c
=
(
5
6
)
(
5
2
14
)
=
3
14
Length of latus rectum =
a
2b
2
=
(
5
6
)
2×4
=
3
4
5
Answer:
The given equation is 5y
2
−9x
2
=36
⇒
(
5
36
)
y
2
−
4
x
2
=1
⇒
(
5
6
)
2
y
2
−
2
2
x
2
=1...(1)
On comparing equation (1) with the standard equation of hyperbola
i.e.,
a
2
y
2
−
b
2
x
2
=1,
we obtain a=
5
6
and b=2
We know that a
2
+b
2
=c
2
, where c=ae
∴c
2
=
5
36
+4=
5
56
⇒c=
5
56
=
5
2
14
Therefore, the coordinates of the foci are (0,±
5
2
14
)
The coordinates of the vertices are (0,±
5
6
)
Eccentricity e=
a
c
=
(
5
6
)
(
5
2
14
)
=
3
14
Length of latus rectum =
a
2b
2
=
(
5
6
)
2×4
=
3
4
5
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