JEE Main · Maths · Conic Sections
Ellipse Eccentricity: JEE Main previous year questions
47 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 21 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 47
- in 41 of 108 shifts
- Years asked
- 7/8
- last asked 2026
- Weighted estimate
- 0.5
- model; history: 0.4 a shift on average, typically 0.2–0.6
Key findings
- 01
Asked in 7 of 8 years with analysed shifts and in 41 of 108 shifts: 47 questions, #63 of 196 topics.
- 02
43% of its questions since 2020 tested an idea no earlier year had asked; 20 repeated an idea from the year before.
- 03
The most repeated idea is Length of Latus Rectum, asked 12 times in 11 shifts (2020, 2022, 2023, 2024, 2025, 2026), most often as “eccentricity from common latus rectum”.
- 04
JEE Main has asked 16 of the 60 ideas in this topic; 39 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (83%); 17% need a numerical answer, 17% are easy and 30% hard. It went up from 0.3 to 0.6 questions a shift since 2024.
- 06
The skill tested most is multi-step (79%), then calculation (17%).
Questions a shift, year by year
Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.
Raw count: 2017: 0 in 1 shift · 2020: 7 in 12 shifts · 2021: 7 in 24 shifts · 2022: 9 in 24 shifts · 2023: 3 in 12 shifts · 2024: 10 in 18 shifts · 2025: 7 in 8 shifts · 2026: 4 in 9 shifts.
- Up to 2023
- 0.3
- a shift, of 25
- Since 2024
- 0.6
- +0.3
- Usual gap
- 1.0 yrs
- between years asking it
- Shifts with it
- 41/108
- 38% of analysed shifts
Revise first
- Length of Latus Rectum · asked 2020, 2022, 2023, 2024, 2025, 2026
- Eccentricity calculation · asked 2020, 2021, 2022, 2023, 2024, 2026
- Focal distance property · asked 2020, 2021, 2022, 2025, 2026
How it is asked
Difficulty, format and skill
Across all 47 questions on Ellipse Eccentricity since 2017.
Difficulty
QUESTIONS- Easy8 · 17%
- Medium25 · 53%
- Hard14 · 30%
Format
SHARE- Single correct · 39 Q83%
- Numerical value · 8 Q17%
Skill tested
SHARE- Multi-step · 37 Q79%
- Calculation · 8 Q17%
- Application · 2 Q4%
Repeats
New idea, or one asked before?
Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 16 of the 60 ideas in this topic. 39 have never been asked yet.
- Asked directly16 · 27%
- Touched inside another question5 · 8%
- Never asked39 · 65%
Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.
Drill down
Chapter, idea, question
Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.
16 ideas inside
Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.
Ideas
Every idea inside this topic
16 different ideas were tested; 6 came more than once.
eccentricity from common latus rectum
Numerical value · 11 shifts · 6 numericalrelation between conic eccentricities
Single correct · 11 shiftscount complex numbers on circle and ellipse
Single correct · 5 shifts · 1 numericaleccentricity of conic through foci of two conics
Single correct · 5 shiftseccentricity from minor axis and foci distance
Single correct · 2 shiftsfocal distances of point on ellipse
Single correct · 2 shiftslatus rectum from eccentricity and point
Single correct · 1 shiftmaximum area of triangle with vertex on circle
Single correct · 1 shiftellipse quantity from axis condition
Single correct · 1 shiftlatus rectum of ellipse from directrix and focus
Single correct · 1 shiftaxes of ellipse from latus rectum and subtended angle
Numerical value · 1 shift · 1 numericaleccentricity from maximum inscribed area
Single correct · 1 shiftarea of focal triangle at tangent point
Single correct · 1 shiftlength of segment cut by tangents on ellipse
Single correct · 1 shiftequal eccentricity of two related ellipses
Single correct · 1 shifteccentricity from normal at latus rectum end
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Length of Latus Rectumeccentricity from common latus rectum | 12 | 11 | Numerical valueMulti-step | 6 | |
| Eccentricity calculationrelation between conic eccentricities | 11 | 11 | Single correctMulti-step | – | |
| Focal distance propertycount complex numbers on circle and ellipse | 5 | 5 | Single correctMulti-step | 1 | |
| Coordinates of focieccentricity of conic through foci of two conics | 5 | 5 | Single correctMulti-step | – | |
| Distance Between Focieccentricity from minor axis and foci distance | 2 | 2 | Single correctCalculation | – | |
| Product of Focal Distancesfocal distances of point on ellipse | 2 | 2 | Single correctMulti-step | – | |
| Vertical Ellipse Latus Rectumlatus rectum from eccentricity and point | 1 | 1 | Single correctCalculation | – | |
| Center to Focus Distancemaximum area of triangle with vertex on circle | 1 | 1 | Single correctMulti-step | – | |
| Eccentricity when Foci Distance Equals Minor Axisellipse quantity from axis condition | 1 | 1 | Single correctCalculation | – | |
| Equations of directriceslatus rectum of ellipse from directrix and focus | 1 | 1 | Single correctMulti-step | – | |
| Eccentricity from Minor Axis Subtended Angleaxes of ellipse from latus rectum and subtended angle | 1 | 1 | Numerical valueMulti-step | 1 | |
| Maximum Inscribed Rectangle Area via Eccentricityeccentricity from maximum inscribed area | 1 | 1 | Single correctMulti-step | – | |
| Area of Foci-Minor Axis Trianglearea of focal triangle at tangent point | 1 | 1 | Single correctMulti-step | – | |
| Intersection of Tangents at Focal Chord Extremitieslength of segment cut by tangents on ellipse | 1 | 1 | Single correctMulti-step | – | |
| Similarity of Ellipsesequal eccentricity of two related ellipses | 1 | 1 | Single correctMulti-step | – | |
| Eccentricity when Normal at LR End Passes Through Minor Axiseccentricity from normal at latus rectum end | 1 | 1 | Single correctMulti-step | – |
Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas
Every question
Ellipse Eccentricity questions, year by year
The newest 40 show their opening words as they appeared in the official paper; older ones name the idea they tested. Open one for its options and the official answer.
JEE Main 20264 questions in 4 shifts
- 2 Apr, Shift 1Q10Let an ellipse , , pass through the point and have eccentricity . Then…
Idea: Vertical Ellipse Latus Rectum
New ideaMediumSingle correct - 4 Apr, Shift 1Q22Consider the parabola and the ellipse . Let the line segment joining the points of…
Idea: Length of Latus Rectum
Asked the year beforeMediumNumerical value - 5 Apr, Shift 1Q9Let a focus of the ellipse be and its eccentricity be . If the point…
Idea: Eccentricity calculation
EasySingle correct - 8 Apr, Shift 2Q2The number of values of , satisfying the equations and…
Idea: Focal distance property
Asked the year beforeHardSingle correct
JEE Main 20257 questions in 6 shifts
- 2 Apr, Shift 1Q4If S and S' are the foci of the ellipse and P be a point on the ellipse, then…
Idea: Product of Focal Distances
New ideaMediumSingle correct - 2 Apr, Shift 2Q12If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the…
Idea: Distance Between Foci
EasySingle correct - 3 Apr, Shift 2Q12Let be the circle of minimum area enclosing the ellipse with eccentricity and…
Idea: Center to Focus Distance
New ideaHardSingle correct - 4 Apr, Shift 2Q11The centre of a circle C is at the centre of the ellipse , . Let C pass through the foci …
Idea: Focal distance property
HardSingle correct - 7 Apr, Shift 2Q12Let the length of a latus rectum of an ellipse be 10. If its eccentricity is the minimum value of the…
Idea: Length of Latus Rectum
Asked the year beforeMediumSingle correct - 7 Apr, Shift 2Q13Let and be the eccentricities of the ellipse and the hyperbola…
Idea: Coordinates of foci
Asked the year beforeMediumSingle correct - 8 Apr, Shift 2Q12Let the ellipse pass through the centre of the circle of radius . Let …
Idea: Product of Focal Distances
New ideaMediumSingle correct
JEE Main 202410 questions in 9 shifts
- 5 Apr, Shift 1Q15Let the line , , intersect the -axis and -axis at the points A and B, respectively. If the equation of the circle…
Idea: Length of Latus Rectum
Asked the year beforeMediumSingle correct - 9 Apr, Shift 1Q12Let , and , . If and denote the eccentricity and the length of the…
Idea: Length of Latus Rectum
Asked the year beforeEasySingle correct - 9 Apr, Shift 2Q15Let the foci of a hyperbola coincide with the foci of the ellipse and the eccentricity of…
Idea: Coordinates of foci
MediumSingle correct - 1 Feb, Shift 1Q12For , if the eccentricity of the hyperbola is times eccentricity of the…
Idea: Eccentricity calculation
Asked the year beforeMediumSingle correct - 1 Feb, Shift 1Q13Let , be an ellipse, whose eccentricity is and the length of the latusrectum…
Idea: Length of Latus Rectum
Asked the year beforeMediumSingle correct - 1 Feb, Shift 2Q13Let be a point on the ellipse . Let the line passing through and parallel to -axis meet the…
Idea: Eccentricity calculation
Asked the year beforeHardSingle correct - 30 Jan, Shift 1Q15If 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 :
Idea: Eccentricity when Foci Distance Equals Minor Axis
New ideaMediumSingle correct - 30 Jan, Shift 2Q14Let and be the points on the line . Let the point divide the line segment internally…
Idea: Equations of directrices
New ideaMediumSingle correct - 31 Jan, Shift 1Q28Let the foci and length of the latus rectum of an ellipse be and ,…
Idea: Length of Latus Rectum
Asked the year beforeMediumNumerical value - 31 Jan, Shift 2Q14Let be a parabola with vertex and directrix . Let an ellipse , of…
Idea: Length of Latus Rectum
Asked the year beforeHardSingle correct
JEE Main 20233 questions in 2 shifts
- 6 Apr, Shift 2Q2In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of…
Idea: Eccentricity calculation
Asked the year beforeEasySingle correct - 6 Apr, Shift 2Q27Let the eccentricity of an ellipse is reciprocal to that of the hyperbola . If the…
Idea: Length of Latus Rectum
Asked the year beforeHardNumerical value - 15 Apr, Shift 1Q28Let an ellipse with centre and latus rectum of length have its major axis along x-axis. If its minor axis subtends…
Idea: Eccentricity from Minor Axis Subtended Angle
New ideaMediumNumerical value
JEE Main 20229 questions in 6 shifts
- 25 Jul, Shift 2Q12If the ellipse meets the line on the -axis and the line…
Idea: Eccentricity calculation
Asked the year beforeEasySingle correct - 25 Jul, Shift 2Q14Let the foci of the ellipse and the hyperbola coincide.…
Idea: Coordinates of foci
Asked the year beforeMediumSingle correct - 27 Jul, Shift 1Q24An ellipse passes through the vertices of the hyperbola…
Idea: Length of Latus Rectum
HardNumerical value - 27 Jul, Shift 1Q29If the length of the latus rectum of the ellipse is 4, and is the length of its major axis, then…
Idea: Length of Latus Rectum
MediumNumerical value - 28 Jul, Shift 2Q83Let the tangents at the points P and Q on the ellipse meet at the point . If S is…
Idea: Focal distance property
Asked the year beforeHardNumerical value - 24 Jun, Shift 2Q9Let the maximum area of the triangle that can be inscribed in the ellipse , , having one of…
Idea: Maximum Inscribed Rectangle Area via Eccentricity
New ideaHardSingle correct - 24 Jun, Shift 2Q29Let the hyperbola and the ellipse be such that the length of latus rectum of is…
Idea: Length of Latus Rectum
MediumNumerical value - 27 Jun, Shift 1Q13Let the eccentricity of an ellipse , , be . If this ellipse passes through the point…
Idea: Eccentricity calculation
Asked the year beforeEasySingle correct - 30 Jun, Shift 1Q15Let the eccentricity of the ellipse be b times the eccentricity of the hyperbola , where a is the…
Idea: Eccentricity calculation
Asked the year beforeHardSingle correct
JEE Main 20217 questions in 7 shifts
- 3 Aug, Shift 1Q74If the tangents at the points on the ellipse, meet the tangent at on it at the…
Idea: Intersection of Tangents at Focal Chord Extremities
New ideaHardSingle correct - 3 Aug, Shift 2Q74If an ellipse passes through the point and has foci at , then its eccentricity is
Idea: Focal distance property
Asked the year beforeMediumSingle correct - 26 Aug, Shift 1Q74On the ellipse let P be a point in the second quadrant such that the tangent at P to the ellipse is…
Idea: Area of Foci-Minor Axis Triangle
New ideaHardSingle correct - 25 Feb, Shift 2Q72A hyperbola passes through the foci of the ellipse and its transverse and conjugate axes coincide…
Idea: Coordinates of foci
New ideaMediumSingle correct - 22 Jul, Shift 2Q67Let , . Let be another ellipse such that it touches the end points of…
Idea: Similarity of Ellipses
New ideaMediumSingle correct - 25 Jul, Shift 1Q61Let an ellipse , , passes through and has eccentricity…
Idea: Eccentricity calculation
Asked the year beforeHardSingle correct - 25 Jul, Shift 2Q76If a tangent to the ellipse meets the tangents at the extremities of its major axis at B and C, then the circle with BC as…
Idea: Coordinates of foci
New ideaHardSingle correct
JEE Main 20207 questions in 7 shifts
- 9 Jan, Shift 1 · Q66Eccentricity calculationNew ideaEasy
- 9 Jan, Shift 2 · Q65Eccentricity calculationNew ideaMedium
- 2 Sep, Shift 2 · Q66Eccentricity calculationNew ideaMedium
- 3 Sep, Shift 2 · Q65Distance Between FociNew ideaMedium
- 4 Sep, Shift 1 · Q65Length of Latus RectumNew ideaMedium
- 5 Sep, Shift 1 · Q65Focal distance propertyNew ideaEasy
- 6 Sep, Shift 2 · Q66Eccentricity when Normal at LR End Passes Through Minor AxisNew ideaMedium
Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.