JEE Main · Maths · Conic Sections

Parabola Focal Chords: JEE Main previous year questions

Name: Parabola Focal Chords: JEE Main previous year questions
Creator: Lumi

12 questions in the 108 JEE Main shifts Lumi analysed, in 6 of 8 years. Pattern: Asked most years. 5 came in 2024–26. Here is how it is asked and which ideas come back.

Questions: 12; in 12 of 108 shifts
Years asked: 6/8; last asked 2026
Chance in a shift: 19%; calibrated model, how we compute it
Weighted estimate: 0.1; model; history: 0.1 a shift on average, typically 0.0–0.1

Key findings

01
Asked in 6 of 8 years with analysed shifts and in 12 of 108 shifts: 12 questions, #172 of 196 topics. The years that asked it were 1.2 apart on average.
02
75% of its questions since 2020 tested an idea no earlier year had asked; 2 repeated an idea from the year before.
03
The most repeated idea is Equation of focal chord, asked 3 times in 3 shifts (2022, 2023), most often as “eccentricity from shared focal chord of two conics”.
04
JEE Main has asked 8 of the 61 ideas in this topic; 48 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 42% hard.
06
The skill tested most is multi-step (92%), then application (8%).

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: 1 in 12 shifts · 2021: 0 in 24 shifts · 2022: 4 in 24 shifts · 2023: 2 in 12 shifts · 2024: 2 in 18 shifts · 2025: 2 in 8 shifts · 2026: 1 in 9 shifts.

Up to 2023: 0.1; a shift, of 25
Since 2024: 0.1; 0.1
Usual gap: 1.2 yrs; between years asking it
Shifts with it: 12/108; 11% of analysed shifts

How it is asked

Difficulty, format and skill

Across all 12 questions on Parabola Focal Chords since 2017.

Difficulty

QUESTIONS

Easy0 · 0%
Medium7 · 58%
Hard5 · 42%

Format

Single correct · 9 Q75%
Numerical value · 3 Q25%

Skill tested

Multi-step · 11 Q92%
Application · 1 Q8%

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.

’17’20’21’22’23’24’25’26

Idea asked for the first time
Idea asked in an earlier year

Coverage of the topic

JEE Main has asked 8 of the 61 ideas in this topic. 48 have never been asked yet.

848

Asked directly8 · 13%
Touched inside another question5 · 8%
Never asked48 · 79%

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

Idea, year, question

Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.

ideaAskedShareYears’17’20’21’22’23’24’25’26

OpenRepeated3 · 25%25%2/82
- 8 Apr ’23 S1 · Q14
  Let $R$ be the focus of the parabola $y^2=20x$ and the line $y=mx+c$ intersect the parabola at two points $P$ and $Q$ . Let the point…
  hardSingle correctAsked the year before
- 29 Jul ’22 S1 · Q17
  Let the focal chord of the parabola $P : y^2 = 4x$ along the line $L : y = mx + c$ , $m > 0$ meet the parabola at the points M and N. Let…
  hardSingle correctNew idea
- 29 Jun ’22 S1 · Q18
  Let PQ be a focal chord of the parabola $y^2 = 4x$ such that it subtends an angle of $\frac{\pi}{2}$ at the point $(3, 0)$ . Let the line…
  hardSingle correctNew idea
OpenRepeated2 · 17%17%2/8
OpenRepeated2 · 17%17%2/8
Open1 · 8%8%1/8
Open1 · 8%8%1/8
Open1 · 8%8%1/8
Open1 · 8%8%1/8
Open1 · 8%8%1/8

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

8 different ideas were tested; 3 came more than once.

Equation of focal chord3×
eccentricity from shared focal chord of two conics
Single correct · 3 shifts
Parameter relation t1*t2 = -12×
area of triangle with parabola focal chord
Single correct · 2 shifts
Focal Chord Length via Slope2×
focal chord length and distance from origin
Numerical value · 2 shifts · 1 numerical
Point of Contact of Focal Radius Circle with Vertex Tangent1×
circle on focal radius touching axis
Single correct · 1 shift
Ratio of Y-Coordinates of Extremities1×
ratio focus divides focal chord
Single correct · 1 shift
Focal Chord Length via Vertex Distance1×
focal chord length and distance from origin
Numerical value · 1 shift · 1 numerical
Chord of Contact from Directrix is Focal1×
chord of contact of perpendicular tangents is focal
Single correct · 1 shift
Length of focal chord1×
area of triangle from focal chord
Numerical value · 1 shift · 1 numerical

Idea	Times	Shifts	Format	Numerical
Equation of focal chordeccentricity from shared focal chord of two conics	3	3	Single correctMulti-step	–
Parameter relation t1*t2 = -1area of triangle with parabola focal chord	2	2	Single correctMulti-step	–
Focal Chord Length via Slopefocal chord length and distance from origin	2	2	Numerical valueMulti-step	1
Point of Contact of Focal Radius Circle with Vertex Tangentcircle on focal radius touching axis	1	1	Single correctMulti-step	–
Ratio of Y-Coordinates of Extremitiesratio focus divides focal chord	1	1	Single correctApplication	–
Focal Chord Length via Vertex Distancefocal chord length and distance from origin	1	1	Numerical valueMulti-step	1
Chord of Contact from Directrix is Focalchord of contact of perpendicular tangents is focal	1	1	Single correctMulti-step	–
Length of focal chordarea of triangle from focal chord	1	1	Numerical valueMulti-step	1

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

Parabola Focal Chords 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.

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.

Key findings

Questions a shift, year by year

Difficulty, format and skill

Difficulty

Format

Skill tested

New idea, or one asked before?

Coverage of the topic

Idea, year, question

Every idea inside this topic

Parabola Focal Chords questions, year by year

JEE Main 20261 question in 1 shift

JEE Main 20252 questions in 2 shifts

JEE Main 20242 questions in 2 shifts

JEE Main 20232 questions in 2 shifts

JEE Main 20224 questions in 4 shifts

JEE Main 20201 question in 1 shift

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