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Page 1
JEE Mains Previous Year Questions
(2021-2024): Ellipse
2024
Q1: Let ?? be a point on the ellipse
?? ?? ?? +
?? ?? ?? = ?? . Let the line passing through ?? and parallel to ?? -axis
meet the circle ?? ?? + ?? ?? = ?? at point ?? such that ?? and ?? are on the same side of the ?? -axis. Then, the
eccentricity of the locus of the point ?? on ???? such that ???? : ???? = ?? : ?? as ?? moves on the ellipse, is:
A.
????
????
B.
v ??????
????
C.
v ????
??
D.
????
????
[JEE Main 2024 (Online) 1st February Evening Shift]
Ans: (c)
h = 3 c o s ? ?? k =
18
7
sin ? ?? ? ? locus =
x
2
9
+
49 y
2
324
= 1
e =
v
1 -
324
49 × 9
=
v 117
21
=
v 13
7
Page 2
JEE Mains Previous Year Questions
(2021-2024): Ellipse
2024
Q1: Let ?? be a point on the ellipse
?? ?? ?? +
?? ?? ?? = ?? . Let the line passing through ?? and parallel to ?? -axis
meet the circle ?? ?? + ?? ?? = ?? at point ?? such that ?? and ?? are on the same side of the ?? -axis. Then, the
eccentricity of the locus of the point ?? on ???? such that ???? : ???? = ?? : ?? as ?? moves on the ellipse, is:
A.
????
????
B.
v ??????
????
C.
v ????
??
D.
????
????
[JEE Main 2024 (Online) 1st February Evening Shift]
Ans: (c)
h = 3 c o s ? ?? k =
18
7
sin ? ?? ? ? locus =
x
2
9
+
49 y
2
324
= 1
e =
v
1 -
324
49 × 9
=
v 117
21
=
v 13
7
Q2: Let
?? ?? ?? ?? +
?? ?? ?? ?? = ?? , ?? > ?? be an ellipse, whose eccentricity is
?? v ?? and the length of the latusrectum is
v ???? . Then the square of the eccentricity of
?? ?? ?? ?? -
?? ?? ?? ?? = ?? is
A. 3
B.
?? ??
C.
?? ??
D.
?? ?? [JEE Main 2024 (Online) 1st February Morning Shift]
Ans: (c)
Explanation: Currently no explanation available
Q3: Let ?? be a parabola with vertex ( ?? , ?? ) and directrix ?? ?? + ?? = ?? . Let an ellipse ?? :
?? ?? ?? ?? +
?? ?? ?? ?? = ?? , ?? >
?? , of eccentricity
?? v ?? pass through the focus of the parabola ?? . Then, the square of the length of the
latus rectum of ?? , is
A.
??????
????
B.
????????
????
C.
??????
??
D.
??????
?? [JEE Main 2024 (Online) 31st January Evening Shift]
Ans: (b)
Page 3
JEE Mains Previous Year Questions
(2021-2024): Ellipse
2024
Q1: Let ?? be a point on the ellipse
?? ?? ?? +
?? ?? ?? = ?? . Let the line passing through ?? and parallel to ?? -axis
meet the circle ?? ?? + ?? ?? = ?? at point ?? such that ?? and ?? are on the same side of the ?? -axis. Then, the
eccentricity of the locus of the point ?? on ???? such that ???? : ???? = ?? : ?? as ?? moves on the ellipse, is:
A.
????
????
B.
v ??????
????
C.
v ????
??
D.
????
????
[JEE Main 2024 (Online) 1st February Evening Shift]
Ans: (c)
h = 3 c o s ? ?? k =
18
7
sin ? ?? ? ? locus =
x
2
9
+
49 y
2
324
= 1
e =
v
1 -
324
49 × 9
=
v 117
21
=
v 13
7
Q2: Let
?? ?? ?? ?? +
?? ?? ?? ?? = ?? , ?? > ?? be an ellipse, whose eccentricity is
?? v ?? and the length of the latusrectum is
v ???? . Then the square of the eccentricity of
?? ?? ?? ?? -
?? ?? ?? ?? = ?? is
A. 3
B.
?? ??
C.
?? ??
D.
?? ?? [JEE Main 2024 (Online) 1st February Morning Shift]
Ans: (c)
Explanation: Currently no explanation available
Q3: Let ?? be a parabola with vertex ( ?? , ?? ) and directrix ?? ?? + ?? = ?? . Let an ellipse ?? :
?? ?? ?? ?? +
?? ?? ?? ?? = ?? , ?? >
?? , of eccentricity
?? v ?? pass through the focus of the parabola ?? . Then, the square of the length of the
latus rectum of ?? , is
A.
??????
????
B.
????????
????
C.
??????
??
D.
??????
?? [JEE Main 2024 (Online) 31st January Evening Shift]
Ans: (b)
Slope of axis =
1
2
?? - 3 =
1
2
( ?? - 2 )
? ? 2 ?? - 6 = ?? - 2
? ? 2 ?? - ?? - 4 = 0
2 ?? + ?? - 6 = 0
4 ?? + 2 ?? - 12 = 0
?? + 1 . 6 = 4 ? ?? = 2 . 4
?? + 2 . 8 = 6 ? ?? = 3 . 2
Ellipse passes through ( 2 . 4 , 3 . 2 )
?
(
24
10
)
2
a
2
+
(
32
10
)
2
b
2
= 1 … .
Also 1 -
b
2
a
2
=
1
2
=
b
2
a
2
=
1
2
? ?? 2
= 2 ?? 2
Put in ( 1 ) ? ?? 2
=
328
25
? (
2 ?? 2
?? )
2
=
4 ?? 2
?? 2
× ?? 2
= 4 ×
1
2
×
328
25
=
656
25
Q4: Let ?? ( ?? , 0 ) and ?? ( 0 , ?? ) be the points on the line 5 ?? + 7 ?? = 50. Let the point ?? divide the line
segment ???? internally in the ratio 7 : 3. Let 3 ?? - 25 = 0 be a directrix of the ellipse ?? :
?? 2
?? 2
+
?? 2
?? 2
= 1 and
the corresponding focus be ?? . If from ?? , the perpendicular on the ?? -axis passes through ?? , then the
length of the latus rectum of ?? is equal to,
A.
25
3
B.
25
9
C.
32
5
D.
32
9
[JEE Main 2024 (Online) 30th January Evening Shift]
Ans: (c)
A = ( 10 , 0 )
B = ( 0 ,
50
7
)
} P = ( 3 , 5 )
Page 4
JEE Mains Previous Year Questions
(2021-2024): Ellipse
2024
Q1: Let ?? be a point on the ellipse
?? ?? ?? +
?? ?? ?? = ?? . Let the line passing through ?? and parallel to ?? -axis
meet the circle ?? ?? + ?? ?? = ?? at point ?? such that ?? and ?? are on the same side of the ?? -axis. Then, the
eccentricity of the locus of the point ?? on ???? such that ???? : ???? = ?? : ?? as ?? moves on the ellipse, is:
A.
????
????
B.
v ??????
????
C.
v ????
??
D.
????
????
[JEE Main 2024 (Online) 1st February Evening Shift]
Ans: (c)
h = 3 c o s ? ?? k =
18
7
sin ? ?? ? ? locus =
x
2
9
+
49 y
2
324
= 1
e =
v
1 -
324
49 × 9
=
v 117
21
=
v 13
7
Q2: Let
?? ?? ?? ?? +
?? ?? ?? ?? = ?? , ?? > ?? be an ellipse, whose eccentricity is
?? v ?? and the length of the latusrectum is
v ???? . Then the square of the eccentricity of
?? ?? ?? ?? -
?? ?? ?? ?? = ?? is
A. 3
B.
?? ??
C.
?? ??
D.
?? ?? [JEE Main 2024 (Online) 1st February Morning Shift]
Ans: (c)
Explanation: Currently no explanation available
Q3: Let ?? be a parabola with vertex ( ?? , ?? ) and directrix ?? ?? + ?? = ?? . Let an ellipse ?? :
?? ?? ?? ?? +
?? ?? ?? ?? = ?? , ?? >
?? , of eccentricity
?? v ?? pass through the focus of the parabola ?? . Then, the square of the length of the
latus rectum of ?? , is
A.
??????
????
B.
????????
????
C.
??????
??
D.
??????
?? [JEE Main 2024 (Online) 31st January Evening Shift]
Ans: (b)
Slope of axis =
1
2
?? - 3 =
1
2
( ?? - 2 )
? ? 2 ?? - 6 = ?? - 2
? ? 2 ?? - ?? - 4 = 0
2 ?? + ?? - 6 = 0
4 ?? + 2 ?? - 12 = 0
?? + 1 . 6 = 4 ? ?? = 2 . 4
?? + 2 . 8 = 6 ? ?? = 3 . 2
Ellipse passes through ( 2 . 4 , 3 . 2 )
?
(
24
10
)
2
a
2
+
(
32
10
)
2
b
2
= 1 … .
Also 1 -
b
2
a
2
=
1
2
=
b
2
a
2
=
1
2
? ?? 2
= 2 ?? 2
Put in ( 1 ) ? ?? 2
=
328
25
? (
2 ?? 2
?? )
2
=
4 ?? 2
?? 2
× ?? 2
= 4 ×
1
2
×
328
25
=
656
25
Q4: Let ?? ( ?? , 0 ) and ?? ( 0 , ?? ) be the points on the line 5 ?? + 7 ?? = 50. Let the point ?? divide the line
segment ???? internally in the ratio 7 : 3. Let 3 ?? - 25 = 0 be a directrix of the ellipse ?? :
?? 2
?? 2
+
?? 2
?? 2
= 1 and
the corresponding focus be ?? . If from ?? , the perpendicular on the ?? -axis passes through ?? , then the
length of the latus rectum of ?? is equal to,
A.
25
3
B.
25
9
C.
32
5
D.
32
9
[JEE Main 2024 (Online) 30th January Evening Shift]
Ans: (c)
A = ( 10 , 0 )
B = ( 0 ,
50
7
)
} P = ( 3 , 5 )
ae = 3
a
e
=
25
3
a = 5
b = 4
Length of ???? =
2 ?? 2
?? =
32
5
Q5: If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then
the eccentricity of the ellipse is:
A.
?? v ??
B.
?? v ??
C.
v ?? ??
D.
v ?? ?? [JEE Main 2024 (Online) 30th January Morning Shift]
Ans: (b)
2 ?? ? = ????
?? ?? ? =
?? 2
?? ? =
v
1 -
?? 2
4
?? ? =
2
v 5
Q6: The length of the chord of the ellipse
?? ?? ????
+
?? ?? ????
= ?? , whose mid point is ( ?? ,
?? ?? ), is equal to:
A.
v ????????
??
B.
v ????????
??
Page 5
JEE Mains Previous Year Questions
(2021-2024): Ellipse
2024
Q1: Let ?? be a point on the ellipse
?? ?? ?? +
?? ?? ?? = ?? . Let the line passing through ?? and parallel to ?? -axis
meet the circle ?? ?? + ?? ?? = ?? at point ?? such that ?? and ?? are on the same side of the ?? -axis. Then, the
eccentricity of the locus of the point ?? on ???? such that ???? : ???? = ?? : ?? as ?? moves on the ellipse, is:
A.
????
????
B.
v ??????
????
C.
v ????
??
D.
????
????
[JEE Main 2024 (Online) 1st February Evening Shift]
Ans: (c)
h = 3 c o s ? ?? k =
18
7
sin ? ?? ? ? locus =
x
2
9
+
49 y
2
324
= 1
e =
v
1 -
324
49 × 9
=
v 117
21
=
v 13
7
Q2: Let
?? ?? ?? ?? +
?? ?? ?? ?? = ?? , ?? > ?? be an ellipse, whose eccentricity is
?? v ?? and the length of the latusrectum is
v ???? . Then the square of the eccentricity of
?? ?? ?? ?? -
?? ?? ?? ?? = ?? is
A. 3
B.
?? ??
C.
?? ??
D.
?? ?? [JEE Main 2024 (Online) 1st February Morning Shift]
Ans: (c)
Explanation: Currently no explanation available
Q3: Let ?? be a parabola with vertex ( ?? , ?? ) and directrix ?? ?? + ?? = ?? . Let an ellipse ?? :
?? ?? ?? ?? +
?? ?? ?? ?? = ?? , ?? >
?? , of eccentricity
?? v ?? pass through the focus of the parabola ?? . Then, the square of the length of the
latus rectum of ?? , is
A.
??????
????
B.
????????
????
C.
??????
??
D.
??????
?? [JEE Main 2024 (Online) 31st January Evening Shift]
Ans: (b)
Slope of axis =
1
2
?? - 3 =
1
2
( ?? - 2 )
? ? 2 ?? - 6 = ?? - 2
? ? 2 ?? - ?? - 4 = 0
2 ?? + ?? - 6 = 0
4 ?? + 2 ?? - 12 = 0
?? + 1 . 6 = 4 ? ?? = 2 . 4
?? + 2 . 8 = 6 ? ?? = 3 . 2
Ellipse passes through ( 2 . 4 , 3 . 2 )
?
(
24
10
)
2
a
2
+
(
32
10
)
2
b
2
= 1 … .
Also 1 -
b
2
a
2
=
1
2
=
b
2
a
2
=
1
2
? ?? 2
= 2 ?? 2
Put in ( 1 ) ? ?? 2
=
328
25
? (
2 ?? 2
?? )
2
=
4 ?? 2
?? 2
× ?? 2
= 4 ×
1
2
×
328
25
=
656
25
Q4: Let ?? ( ?? , 0 ) and ?? ( 0 , ?? ) be the points on the line 5 ?? + 7 ?? = 50. Let the point ?? divide the line
segment ???? internally in the ratio 7 : 3. Let 3 ?? - 25 = 0 be a directrix of the ellipse ?? :
?? 2
?? 2
+
?? 2
?? 2
= 1 and
the corresponding focus be ?? . If from ?? , the perpendicular on the ?? -axis passes through ?? , then the
length of the latus rectum of ?? is equal to,
A.
25
3
B.
25
9
C.
32
5
D.
32
9
[JEE Main 2024 (Online) 30th January Evening Shift]
Ans: (c)
A = ( 10 , 0 )
B = ( 0 ,
50
7
)
} P = ( 3 , 5 )
ae = 3
a
e
=
25
3
a = 5
b = 4
Length of ???? =
2 ?? 2
?? =
32
5
Q5: If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then
the eccentricity of the ellipse is:
A.
?? v ??
B.
?? v ??
C.
v ?? ??
D.
v ?? ?? [JEE Main 2024 (Online) 30th January Morning Shift]
Ans: (b)
2 ?? ? = ????
?? ?? ? =
?? 2
?? ? =
v
1 -
?? 2
4
?? ? =
2
v 5
Q6: The length of the chord of the ellipse
?? ?? ????
+
?? ?? ????
= ?? , whose mid point is ( ?? ,
?? ?? ), is equal to:
A.
v ????????
??
B.
v ????????
??
C.
v ????????
??
D.
v ????????
?? [JEE Main 2024 (Online) 27th January Morning Shift]
Ans: (a)
Explanation: Currently no explanation available
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