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Byju's Answer
Standard XII
Mathematics
Eccentricity of Ellipse
The locus of ...
Question
The locus of mid-point of focal chords of the ellipse
x
2
a
2
+
y
2
b
2
=
1
is:
A
x
2
a
2
+
y
2
b
2
=
e
x
a
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B
x
2
a
2
−
y
2
b
2
=
e
x
a
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C
x
2
+
y
2
=
a
2
+
b
2
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D
None of these
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Solution
The correct option is
A
x
2
a
2
+
y
2
b
2
=
e
x
a
Let
(
h
,
k
)
be the mid point of a focal chord. Then its equation is
T
=
S
1
⇒
x
h
a
2
+
k
y
b
2
−
1
=
h
2
a
2
+
k
2
b
2
−
1
Since it passes through
(
a
e
,
0
)
∴
h
a
e
a
2
=
h
2
a
2
+
k
2
b
2
∴
Locus of
(
h
,
k
)
is
x
2
a
2
+
y
2
b
2
=
x
e
a
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1
Similar questions
Q.
The locus of the mid-points of chords of the ellipse
x
2
a
2
+
y
2
b
2
=
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that touch the circle
x
2
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=
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, is:
Q.
p
(
θ
)
,
D
(
θ
+
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)
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x
2
a
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+
y
2
b
2
=
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Then the locus of point of intersection of the two tangents at P and D to the ellipse is
Q.
If tangent to
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2
a
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+
y
2
b
2
=
1
meets the axes at
A
and
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,
then the locus of mid point of
A
B
is
Q.
Find the locus of the mid point of focal chords of the ellipse
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2
a
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+
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Q.
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is
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Standard XII Mathematics
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