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Byju's Answer
Standard XII
Mathematics
Latus Rectum of Hyperbola
Find the cent...
Question
Find the centre, foci, eccentricity, equation of the directrices, length of the latus rectum of the hyperbola
x
2
−
4
y
2
=
4.
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Solution
Given equation of hyperbola-
x
2
−
4
y
2
=
4
⇒
x
2
4
−
y
2
1
=
1
here
a
=
2
,
b
=
1
Centre of the hyperbola
=
(
0
,
0
)
Eccentricity
(
e
)
=
√
1
+
b
2
a
2
=
√
1
+
1
4
=
√
5
2
Focii of hyperbola
=
(
±
a
e
,
0
)
=
(
±
√
5
,
0
)
Length of latus rectum
(
l
)
=
2
b
2
a
=
2
×
1
2
=
1
Equation of directrices-
x
=
±
a
e
⇒
x
=
±
4
√
5
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1
Similar questions
Q.
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x
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Q.
Find the eccentricity, foci, length of the Latus rectum and the equations of directrices of the ellipse
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Q.
Find the eccentricity, foci, centre, length of latus rectum vertices and the equation to the directrices of the hyperbola.
(a)
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(b)
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=
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Q.
Find the eccentricity, foci and the length of the latus-rectum of the ellipse
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