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Byju's Answer
Standard XII
Mathematics
Focal Chord
α and β are...
Question
α
and
β
are the eccentric angles of the extremities of a focal chord of the ellipse
x
2
a
2
+
y
2
b
2
=
1
, then
cos
2
(
α
−
β
2
)
cos
2
(
α
+
β
2
)
=
A
a
2
+
b
2
a
2
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B
a
2
a
2
+
b
2
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C
a
2
a
2
−
b
2
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D
a
2
−
b
2
a
2
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Solution
The correct option is
B
a
2
−
b
2
a
2
(
α
,
β
)
are eccentric angles of extremities of focal chord.
Equation of chord with
(
α
,
β
)
as extremities is
x
a
cos
(
α
+
β
2
)
+
y
b
sin
(
α
+
β
2
)
=
cos
(
α
−
β
2
)
Since, it passes through
(
a
e
,
0
)
e
cos
(
α
+
β
2
)
=
cos
(
α
−
β
2
)
cos
2
(
α
−
β
2
)
cos
2
(
α
+
β
2
)
=
e
2
=
a
2
−
b
2
a
2
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1
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