JEE Main · Maths · Conic Sections
Power of a Point: JEE Main previous year questions
10 questions in the 108 JEE Main shifts Lumi analysed, in 6 of 8 years. Pattern: Asked most years. 3 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 10
- in 10 of 108 shifts
- Years asked
- 6/8
- last asked 2026
- 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 10 of 108 shifts: 10 questions, #179 of 196 topics. The years that asked it were 1.2 apart on average.
- 02
50% of its questions since 2020 tested an idea no earlier year had asked; 1 repeated an idea from the year before.
- 03
The most repeated idea is Length of Common Chord via Radical Axis, asked 3 times in 3 shifts (2020, 2022, 2024), most often as “common chord of intersecting circles”.
- 04
JEE Main has asked 5 of the 60 ideas in this topic; 49 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (60%); 40% need a numerical answer, 10% are easy and 30% hard.
- 06
The skill tested most is multi-step (60%), then calculation (30%).
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: 2 in 12 shifts · 2021: 3 in 24 shifts · 2022: 1 in 24 shifts · 2023: 1 in 12 shifts · 2024: 2 in 18 shifts · 2025: 0 in 8 shifts · 2026: 1 in 9 shifts.
- Up to 2023
- 0.1
- a shift, of 25
- Since 2024
- 0.1
- 0.0
- Usual gap
- 1.2 yrs
- between years asking it
- Shifts with it
- 10/108
- 9% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 10 questions on Power of a Point since 2017.
Difficulty
QUESTIONS- Easy1 · 10%
- Medium6 · 60%
- Hard3 · 30%
Format
SHARE- Single correct · 6 Q60%
- Numerical value · 4 Q40%
Skill tested
SHARE- Multi-step · 6 Q60%
- Calculation · 3 Q30%
- Application · 1 Q10%
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 5 of the 60 ideas in this topic. 49 have never been asked yet.
- Asked directly5 · 8%
- Touched inside another question6 · 10%
- Never asked49 · 82%
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.
5 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
5 different ideas were tested; 3 came more than once.
common chord of intersecting circles
Numerical value · 3 shifts · 2 numericalcommon chord of two circles and distance of point
Single correct · 3 shifts · 1 numericalmaximise chord distance sum from external point
Single correct · 2 shiftslocus of point with fixed distance ratio
Numerical value · 1 shift · 1 numericalrange of constant for circle position conditions
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Length of Common Chord via Radical Axiscommon chord of intersecting circles | 3 | 3 | Numerical valueMulti-step | 2 | |
| Radical axis of two circlescommon chord of two circles and distance of point | 3 | 3 | Single correctMulti-step | 1 | |
| Secant-Tangent Power Theoremmaximise chord distance sum from external point | 2 | 2 | Single correctApplication | – | |
| Locus of Constant Tangent Ratiolocus of point with fixed distance ratio | 1 | 1 | Numerical valueCalculation | 1 | |
| Point position relative to circlerange of constant for circle position conditions | 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
Power of a Point 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 20261 question in 1 shift
- 5 Apr, Shift 2Q11Let the point P be the vertex of the parabola . If a line passing through the point P intersects the circle…
Idea: Secant-Tangent Power Theorem
HardSingle correct
JEE Main 20242 questions in 2 shifts
- 5 Apr, Shift 2Q15Let the circle and be a circle having centre at and radius 2. If the line of the common chord…
Idea: Radical axis of two circles
Asked the year beforeEasySingle correct - 30 Jan, Shift 2Q28Consider two circles and , where . Let the angle between the two…
Idea: Length of Common Chord via Radical Axis
HardNumerical value
JEE Main 20231 question in 1 shift
- 13 Apr, Shift 1Q21Let , . Let be the circle C of radius 1 in the first quadrant…
Idea: Radical axis of two circles
HardNumerical value
JEE Main 20221 question in 1 shift
- 28 Jun, Shift 2Q23If one of the diameters of the circle is a chord of the circle…
Idea: Length of Common Chord via Radical Axis
MediumNumerical value
JEE Main 20213 questions in 3 shifts
- 24 Feb, Shift 2Q82Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (5, 0). If the locus of the…
Idea: Locus of Constant Tangent Ratio
New ideaMediumNumerical value - 26 Feb, Shift 1Q66In the circle given below, let unit, unit and . Then, the area of the triangle (in square units) is :
Idea: Secant-Tangent Power Theorem
New ideaMediumSingle correct · figure - 22 Jul, Shift 2Q71Let the circle be such that it neither intersects nor touches the co-ordinate axes. If the…
Idea: Point position relative to circle
New ideaMediumSingle correct
JEE Main 20202 questions in 2 shifts
- 3 Sep, Shift 2Q64Let the latus ractum of the parabola be the common chord to the circles and each of them having radius .…
Idea: Length of Common Chord via Radical Axis
New ideaMediumSingle correct - 4 Sep, Shift 2Q65The circle passing through the intersection of the circles, and , having its centre on the line,…
Idea: Radical axis of two circles
New ideaMediumSingle 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.