Parabola is considered as moderate topic that comes under Coordinate geometry chapter and commonly asked in the JEE Advanced Exam 2025. The topic carries approximately 2-3% weightage and candidates can expect 1 to 2 questions from this section in the exam.
The Coordinate geometry section has a graphical representation of geometric figures and questions related to distance, slope, and area. The most asked topics in coordinate geometry are straight lines, circles, parabolas, ellipses, and hyperbolas.
Must Read Articles:
- Download JEE Advanced Last 10 year PYQ for Free
- Download JEE 2024 Question Paper with Detailed Solutions
- JEE Advanced 2025 Syllabus
Listed below the most repeated questions JEE Advanced Previous Year Questions (PYQs) for Parabola along with detailed solutions:
Question 1:
Let the circles
C1:x2+y2=9 and C2:(x??3)2+(y??4)2=16, intersect at the points X and Y. Suppose that another circle C3:(x??h)2+(y??k)2=r2 satisfies the following conditions:
(i) centre of C3 is collinear with the centres of C1 and C2,
(ii)C1 and C2 both lie inside , and
(iii)C3 Touches C1 at M and C2 at N.
Let the line through X and Y intersect C3 at Z and W, and let a common tangent of C1 and C3 be a tangent to the parabola x2=8ay. There are some expressions given in the List-I whose values are given in List-II below: Which of the following is the only INCORRECT combination?
- (I),(P)
- (IV), (U)
- (III), (R)
- (IV), (S)
Question 2:
Let A1, B1, C1 be three points in the xy -plane. Suppose that the lines A1C1 and B1C1 are tangents to the curve y2 = 8x at A1 and B1, respectively. If O = (0,0) and C1 = −( 4, 0), then which of the following statements is (are) TRUE ?
- The length of the line segment OA1 is 43
- The length of the line segment A1B1 is 16
- The orthocenter of the triangle A1B1C1 is (0, 0)
- The orthocenter of the triangle A1B1C1 is (1, 0)
Question 3:
Let
S={(x,y)∈R×R:x≥0,y≥0,y2≤12−2x and 3y+8 x≤58}
Question 4:
Let the straight line y = 2x touch a circle with center (0, α), α > 0, and radius r at a point A1. Let B1 be the point on the circle such that the line segment A1B1 is a diameter of the circle. Let α+r=5+5.
Match each entry in List-I to the correct entry in List-II.
| List - I | List - II | ||
|---|---|---|---|
| (P) | α equals | (1) | (-2, 4) |
| (Q) | r equals | (2) | 55 |
| (R) | A1 equals | (3) | (-2, 6) |
| (S) | B1 equals | (4) | 5 |
| (5) | (2, 4) | ||
The correct option is
Question 5:
Consider a triangle Δ whose two sides lie on the x-axis and the line x+y+1=0. If the orthocenter of Δ is (1, 1), then the equation of the circle passing through the vertices of the triangle Δ is;
- x2 + y2 – 3x + y = 0
- x2 + y2 + x + 3y = 0
- x2 + y2 + 2y – 1 = 0
- x2 + y2 + x + y = 0
JEE Advanced Exam Pattern 2025
- Mode of the exam: The examination was conducted ONLY in the Computer Based Test (CBT) mode.
- Number of papers: Two question papers: Paper 1 and Paper 2 of three hours duration each. Both papers are compulsory.
- Language: English and Hindi
- Total duration: 6 hours
- Number of sections: Each question paper consisted of three separate sections, viz., Physics, Chemistry and Mathematics.
- Marking scheme: Details of the marking scheme were provided in the “Instructions to Candidates” section at the time of examination. The same is also explained further below.
JEE Advanced 2025 Mathematics Syllabus
JEE Advanced Mathematics Syllabus consists of nine units- Sets, Relations and Functions ; Algebra ; Matrices; Probability and Statistics; Trignometry; Analytical Geometry; Differential Calculus ; Integral Calculus and Vectors. Check JEE Advanced 2025 Syllabus
JEE Advanced Mathematics Syllabus according to the seven units is defined below.
| Units | Sub Units |
|---|---|
| Sets, Relations, and Functions | - Sets and their representations, different kinds of sets (empty, finite, and infinite), algebra of sets, intersection, complement, difference, and symmetric difference of sets and their algebraic properties, De-Morgan’s laws on union, intersection, and difference (for finite number of sets), and practical problems based on them.- Cartesian product of finite sets, ordered pair, relations, domain, and codomain of relations, equivalence relation.- Function as a special case of relation, functions as mappings, domain, codomain, range of functions, invertible functions, even and odd functions, into, onto and one-to-one functions, special functions (polynomial, trigonometric, exponential, logarithmic, power, absolute value, greatest integer, etc.), sum, difference, product, and composition of functions. |
| Algebra | - Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.- Statement of fundamental theorem of algebra, quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.- Arithmetic and geometric progressions, arithmetic and geometric means, sums of finite arithmetic and geometric progressions, infinite geometric series, sum of the first n natural numbers, sums of squares and cubes of the first n natural numbers.- Logarithms and their properties, permutations and combinations, binomial theorem for a positive integral index, properties of binomial coefficients. |
| Matrices | - Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, elementary row and column transformations, determinant of a square matrix of order up to three, adjoint of a matrix, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric, and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables. |
| Probability and Statistics | - Random experiment, sample space, different types of events (impossible, simple, compound), addition and multiplication rules of probability, conditional probability, independence of events, total probability, Bayes Theorem, computation of probability of events using permutations and combinations.- Measure of central tendency and dispersion, mean, median, mode, mean deviation, standard deviation, and variance of grouped and ungrouped data, analysis of the frequency distribution with the same mean but different variance, random variable, mean, and variance of the random variable. |
| Trigonometry | - Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.- Inverse trigonometric functions (principal value only) and their elementary properties. |
| Analytical Geometry | - Topics related to coordinate geometry, straight lines, circles, conic sections, and other geometric properties. |
| Differential Calculus | - Concepts of limits, continuity, differentiation, derivatives of functions, application of derivatives, increasing and decreasing functions, maxima and minima. |
| Integral Calculus | - Indefinite and definite integrals, properties of integrals, fundamental theorem of calculus, methods of integration, applications of integration. |
| Vectors | - Vectors and their properties, operations on vectors, scalar and vector products, applications in geometry and physics. |
JEE Advanced Mathematics Chapter-wise Weightage
However, based on the previous year's analysis, the chapters along with the number of questions and marks tabulated below:
| Chapter Name | Number of Questions | Marks |
|---|---|---|
| Application of Derivatives | 3 | 9 |
| Ellipse | 1 | 3 |
| Circles | 2 | 6 |
| Parabola | 2 | 7 |
| Definite Integral | 2 | 7 |
| Permutations and Combinations | 1 | 3 |
| Sequence and Series | 1 | 3 |
| Matrices | 2 | 7 |
| Limit and Continuity | 1 | 4 |
| Probability | 1 | 4 |
| Complex Numbers | 1 | 4 |
| Hyperbola | 1 | 4 |
JEE Advanced - Marks wise Weightage of Topics
| Topics | Marks |
|---|---|
| Calculus | 40-50 marks |
| Vector and 3D Geometry | 15-20 marks |
| Probability & Permutation & Combination | 15-20 marks |
| Parabola, Hyperbola, Ellipse, Rectangular Hyperbola | 15 marks |
| Complex Numbers | 15 marks |
Important Books for Mathematics:
JEE Advanced 2024 Question Paper PDF with Solutions
| Paper Name | Question Paper Link | Solutions Link |
|---|---|---|
| JEE Advanced 2024 Paper 1 Question Paper (English) | Download PDF | Check Solutions |
| JEE Advanced 2024 Paper 2 Question Paper (English) | Download PDF | Check Solutions |
| JEE Advanced 2024 Paper 1 Question Paper (Hindi) | Download PDF | Check Solutions |
| JEE Advanced 2024 Paper 1 Question Paper (Hindi) | Download PDF | Check Solutions |
JEE Advanced Last 5 Year Mathematics Papers Pdf
Download free JEE Advanced Previous Year Question Paper PDFs from the table provided below:-
| JEE Advanced Paper Name | Question Paper Link |
|---|---|
| JEE Advanced 2024 Question Paper PDF | Click Here |
| JEE Advanced 2023 Question Paper PDF | Click Here |
| JEE Advanced 2022 Question Paper PDF | Click Here |
| JEE Advanced 2021 Question Paper PDF | Click Here |
| JEE Advanced 2020 Question Paper PDF | Click Here |
| JEE Advanced 2019 Question Paper PDF | Click Here |
| JEE Advanced 2018 Question Paper PDF | Click Here |
| JEE Advanced 2017 Question Paper PDF | Click Here |
| JEE Advanced 2016 Question Paper PDF | Click Here |
JEE Advanced 2023 Question Paper PDF Download With Solutions
| Paper | Question Paper PDF | Answer Key PDF |
|---|---|---|
| Question Paper 1 PDF | Download PDF | Check Solutions |
| Question Paper 2 PDF | Download PDF | Check Solutions |
| Question Paper AAT PDF | Download PDF | Check Solutions |
JEE Advanced 2022 Question Paper
| 2022 Question Paper | PDF Download |
|---|---|
| Question Paper 1 PDF | Click here |
| Question Paper 2 PDF | Click here |
JEE Advanced 2021 Question Paper
| Question Paper | PDF Download | ||
|---|---|---|---|
| Question Paper 1 PDF | Physics | Chemistry | Maths |
| Question Paper 2 PDF | Physics | Chemistry | Maths |
JEE Advanced 2020 Question Paper
| Question Paper | PDF Download |
| Question Paper 1 PDF | Click here |
| Question Paper 2 PDF | Click here |
Frequently Asked Questions
Q1. Is parabola a part of Coordinate geometry?
Yes, Parabola is a sub-topic of coordinate geometry and are related fields in mathematics but have different applications. Geometry questions can be more complex and may involve multiple concepts, including the use of parabolas in conjunction with other conic sections.
Q2. What are the basic things in coordinate geometry?
The fundamental concepts and basic things in coordinate geometry are as follows:
1. Cartesian Coordinate system: It consists of two perpendicular axes the x-axis and y-axis intersecting at the origin (0,0).. This system helps in plotting points and solving geometric problems.
2. Points and Coordinates: A point is represented as (x,y)(x, y)(x,y), where x indicates the horizontal position (abscissa) and y denotes the vertical position (ordinate).
3. Distance formula; This formula calculates the distance between two points.
Q3. What is a safe score for JEE Advanced exam?
Fundamentally safe score in JEE Advanced 2025 is reliant, on difficulty level and cutoff patterns. In general, 40-50% of total marks can fetch a rank within the IIT admission category. For any top IITs (IIT Bombay, IIT Delhi, IIT Madras), a rank below 2500 is desired. Monitor the category-wise cutoff patterns and last year JEE Advanced cutoffs.
Q4. What is the difficulty level of JEE Advanced ?
JEE Advanced is particularly famous for being of high difficulty, challenging the conceptual clarity, application-based solving of problems, and time management. The mathematics part includes higher-order algebra, calculus, and coordinate geometry; physics demands an understanding of electromagnetism, mechanics, and modern physics at a deeper level; and chemistry has a combination of organic reaction mechanisms, physical chemistry calculations, and inorganic memorization. The test aims to check critical thinking and application of multiple concepts.
Comments