JEE Main · Maths · Conic Sections
Normals to Conics: JEE Main previous year questions
16 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 2 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 16
- in 15 of 108 shifts
- Years asked
- 7/8
- last asked 2025
- Weighted estimate
- 0.1
- model; history: 0.2 a shift on average, typically 0.0–0.3
Key findings
- 01
Asked in 7 of 8 years with analysed shifts and in 15 of 108 shifts: 16 questions, #155 of 196 topics. The years that asked it were 1.3 apart on average. Last asked in 2025.
- 02
53% of its questions since 2020 tested an idea no earlier year had asked; 4 repeated an idea from the year before.
- 03
The most repeated idea is Hyperbola Normal Point Form, asked 6 times in 6 shifts (2020, 2022, 2023), most often as “distance of point from normal to conic”.
- 04
JEE Main has asked 7 of the 55 ideas in this topic; 46 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (75%); 25% need a numerical answer, 0% are easy and 38% hard. It went down from 0.3 to 0.1 questions a shift since 2024.
- 06
The skill tested most is multi-step (88%), then calculation (6%).
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: 1 in 1 shift · 2020: 4 in 12 shifts · 2021: 3 in 24 shifts · 2022: 5 in 24 shifts · 2023: 1 in 12 shifts · 2024: 1 in 18 shifts · 2025: 1 in 8 shifts · 2026: 0 in 9 shifts.
- Up to 2023
- 0.3
- a shift, of 25
- Since 2024
- 0.1
- -0.3
- Usual gap
- 1.3 yrs
- between years asking it
- Shifts with it
- 15/108
- 14% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 16 questions on Normals to Conics since 2017.
Difficulty
QUESTIONS- Easy0 · 0%
- Medium10 · 63%
- Hard6 · 38%
Format
SHARE- Single correct · 12 Q75%
- Numerical value · 4 Q25%
Skill tested
SHARE- Multi-step · 14 Q88%
- Calculation · 1 Q6%
- Application · 1 Q6%
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 7 of the 55 ideas in this topic. 46 have never been asked yet.
- Asked directly7 · 13%
- Touched inside another question2 · 4%
- Never asked46 · 84%
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.
7 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
7 different ideas were tested; 4 came more than once.
distance of point from normal to conic
Single correct · 6 shifts · 2 numericalnormal to ellipse from eccentricity and directrix
Single correct · 3 shiftsnormal intercepts of parabola from tangent condition
Numerical value · 2 shifts · 1 numericalintersection of hyperbola normals
Numerical value · 2 shifts · 1 numericalsmallest circle touching two parabolas
Single correct · 1 shiftshortest distance from point to parabola
Single correct · 1 shiftnormal through point then tangent meets directrix
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Hyperbola Normal Point Formdistance of point from normal to conic | 6 | 6 | Single correctMulti-step | 2 | |
| Ellipse Normal Point Formnormal to ellipse from eccentricity and directrix | 3 | 3 | Single correctMulti-step | – | |
| Parabola Normal Point Formnormal intercepts of parabola from tangent condition | 2 | 2 | Numerical valueMulti-step | 1 | |
| Hyperbola Normal Parametric Formintersection of hyperbola normals | 2 | 2 | Numerical valueMulti-step | 1 | |
| Shortest Distance via Common Normalsmallest circle touching two parabolas | 1 | 1 | Single correctMulti-step | – | |
| Shortest Distance from Point to Parabolashortest distance from point to parabola | 1 | 1 | Single correctCalculation | – | |
| Parabola Normal Parametric Formnormal through point then tangent meets directrix | 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
Normals to Conics questions, year by year
The opening words of each question as it appeared in the official paper, with the idea it tested. Open one for its options and the official answer.
JEE Main 20251 question in 1 shift
- 3 Apr, Shift 1Q11The radius of the smallest circle which touches the parabolas and is
Idea: Shortest Distance via Common Normal
New ideaHardSingle correct
JEE Main 20241 question in 1 shift
- 27 Jan, Shift 1Q10If the shortest distance of the parabola from the centre of the circle is d, then is equal to :
Idea: Shortest Distance from Point to Parabola
New ideaMediumSingle correct
JEE Main 20231 question in 1 shift
- 11 Apr, Shift 2Q27Let the tangent to the parabola at the point be perpendicular to the line . Then the square of…
Idea: Hyperbola Normal Point Form
Asked the year beforeHardNumerical value
JEE Main 20225 questions in 4 shifts
- 26 Jul, Shift 1Q13Let the tangent drawn to the parabola at the point is perpendicular to the line . Then the…
Idea: Hyperbola Normal Point Form
MediumSingle correct - 26 Jul, Shift 1Q29Let the function , , be decreasing in and increasing in . A tangent to…
Idea: Parabola Normal Point Form
Asked the year beforeHardNumerical value - 25 Jun, Shift 2Q29Let the eccentricity of the hyperbola be . If the equation of the normal at the point…
Idea: Hyperbola Normal Point Form
HardNumerical value - 26 Jun, Shift 1Q13Let the normal at the point P on the parabola pass through the point . If the tangent at P to the parabola intersects…
Idea: Parabola Normal Parametric Form
New ideaMediumSingle correct - 26 Jun, Shift 2Q13The normal to the hyperbola at the point on it passes through the point :
Idea: Hyperbola Normal Point Form
MediumSingle correct
JEE Main 20213 questions in 3 shifts
- 4 Aug, Shift 2Q74Let the normal at any point of hyperbola intersect the coordinate axes at points P and Q. Then the…
Idea: Hyperbola Normal Parametric Form
New ideaHardSingle correct - 27 Aug, Shift 1Q70A tangent and a normal are drawn at the point on the parabola , which meet the directrix of the parabola at the points…
Idea: Parabola Normal Point Form
New ideaMediumSingle correct - 27 Aug, Shift 2Q86Let and , where , be two points on the hyperbola…
Idea: Hyperbola Normal Parametric Form
New ideaHardNumerical value
JEE Main 20204 questions in 4 shifts
- 8 Jan, Shift 1Q64Let the line and the ellipse intersect at a point P in the first quadrant. If the normal to this ellipse at P meets…
Idea: Ellipse Normal Point Form
Asked the year beforeMediumSingle correct - 8 Jan, Shift 2Q65If a hyperbola passes through the point and it has vertices at , then the equation of the normal to it at…
Idea: Hyperbola Normal Point Form
New ideaMediumSingle correct - 4 Sep, Shift 1Q66Let P(3, 3) be a point on the hyperbola, . If the normal to it at P intersects the -axis at (9,…
Idea: Hyperbola Normal Point Form
New ideaMediumSingle correct - 4 Sep, Shift 2Q66Let be a directrix to an ellipse whose centre is at the origin and its eccentricity is . If P(1, ), …
Idea: Ellipse Normal Point Form
Asked the year beforeMediumSingle correct
JEE Main 20171 question in 1 shift
- 2 Apr (offline)Q80The eccentricity of an ellipse whose centre is at the origin is . If one of its directrices is , then the equation of…
Idea: Ellipse Normal Point Form
MediumSingle correct
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.