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Byju's Answer
Standard XII
Mathematics
Length of Latus Rectum
PSP1 is focal...
Question
P
S
P
1
is focal chord of the ellipse
4
x
2
+
9
y
2
=
36
. If SP
=
4
then
S
P
1
is
A
2
3
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B
3
5
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C
4
3
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D
4
5
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Solution
The correct option is
D
4
5
Equation of ellipse,
x
2
9
+
y
2
4
=
1
a
=
3
,
b
=
2
.
As we know that,
semi latus rectum is the Harmonic mean of segments
P
S
and
S
P
1
of focal chord,
Mathematically,
b
2
a
=
2
(
S
P
)
(
S
P
′
)
S
P
+
S
P
1
2
2
3
=
2
(
4
)
(
S
P
′
)
4
+
S
P
1
16
+
4
S
P
1
=
24
S
P
1
S
P
1
=
4
5
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Similar questions
Q.
P
S
Q
is a focal chord of the ellipse
4
x
2
+
9
y
2
=
36
such that
S
P
=
4
. If
S
′
is the another focus, write the value of
S
′
Q
Q.
P
S
P
′
is focal chord of the ellipse
4
x
2
+
9
y
2
=
36
. lf
S
P
=
4
then
S
P
′
:
(Note :
S
is a focus and
P
and
P
′
are points on the ellipse)
Q.
The eccentricity of the ellipse
4
x
2
+
9
y
2
+
8
x
+
36
y
+
4
=
0
is
Q.
PSQ is a focal choed of the ellipse
4
x
2
+
9
y
2
=
36
such that SP= 4. If S is the another focus, write the value of SQ.
Q.
PSQ is a focal chord of the ellipse
x
2
4
+
y
2
9
= 1 then
1
S
P
+
1
S
Q
=
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