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Byju's Answer
Standard XII
Mathematics
Chord with a Given Mid Point : Hyperbola
Determine the...
Question
Determine the position of the point (3, - 4) with respect to the
hyperbola
x
2
9
−
y
2
16
=
1
A
Inside
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B
Outside
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C
on the periphery
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D
None of these
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Solution
The correct option is
B
Outside
The given Hyperbola is
x
2
9
−
y
2
16
=
1
or
x
2
9
−
y
2
16
−
1
=
0
Then any point
P
(
x
1
,
y
1
)
will lie inside, on or the outside of the hyperbola
x
2
9
−
y
2
16
=
1
depending upon the value of
(
x
2
1
9
−
y
2
1
16
−
1
)
If the value of
x
2
1
9
−
y
2
1
16
−
1
>
0
then point
P
(
x
1
,
y
1
)
lies inside of the hyperbola.
If the value of
x
2
1
9
−
y
2
1
16
−
1
=
0
then point
P
(
x
1
,
y
1
)
lies on the hyperbola.
If the value of
x
2
1
9
−
y
2
1
16
−
1
<
0
then point
P
(
x
1
,
y
1
)
lies outside of the hyperbola.
Now let the value of the term
x
2
1
9
−
y
2
1
16
−
1
at given point
(
3
,
−
4
)
is
(
x
2
1
9
−
y
2
1
16
−
1
)
(
3
,
−
4
)
Then
(
x
2
1
9
−
y
2
1
16
−
1
)
(
3
,
−
4
)
=
3
2
9
−
(
−
4
)
2
16
−
1
→
1
−
1
−
1
=
−
1
.
.
.
.
.
(
<
0
)
As value of term
x
2
1
9
−
y
2
1
16
−
1
at point
P
(
3
,
−
4
)
is less than
0
, Hence the point lies outside of the hyperbola.
So correct option is
B
Suggest Corrections
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