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Byju's Answer
Standard XII
Mathematics
Position of a Point W.R.T Ellipse
Let 5x2+7y2...
Question
Let
5
x
2
+
7
y
2
=
140
, then
(
0
,
0
)
is:
A
Inside the ellipse
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B
On the ellipse
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C
Outside the ellipse
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D
Centre of the ellipse
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Solution
The correct options are
A
Inside the ellipse
D
Centre of the ellipse
Equation of ellipse
5
x
2
+
7
y
2
=
140
Dividing both sides by
140
x
2
28
+
y
2
20
=
1
Comparing with
(
x
−
h
)
2
a
2
+
(
y
−
k
)
2
b
2
=
1
(
h
,
k
)
=
(
0
,
0
)
Hence (0,0) is centre of given ellipse and it inside the ellipse.
Suggest Corrections
0
Similar questions
Q.
Assertion :The point P
(
1
,
−
3
)
lies inside the ellipse
5
x
2
+
7
y
2
=
140
Reason: Let
S
=
5
x
2
+
7
y
2
−
140
and point P be
(
1
,
−
3
)
then
S
1
>
0
Q.
The point (4,-3) lies inside the ellipse
5
x
2
+
7
y
2
=
140
.
Q.
Assertion :The point P
(
4
,
−
3
)
lies outside the ellipse
5
x
2
+
7
y
2
=
140
Reason: Let
S
1
=
5
x
2
+
7
y
2
−
140
and point P be
(
4
,
−
3
)
then
S
1
>
0
Q.
Let
5
x
2
+
7
y
2
=
140
, then
Position of
(
4
,
−
3
)
relative to the ellipse is
Q.
Let
5
x
2
+
7
y
2
=
140
, then
(
3
,
−
4
)
is:
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