Ellipse carries around 3-4% weightage under the JEE Advanced 2025 exam according to the new JEE Advanced 2025 syllabus and previous years trends. The topic is considered moderate as per conceptual depth.
It is defined as an oval shaped closed curve in which the sum of the distance from the two fixed points (focus) together called Foci at any point is constant and this sub-topic of coordinate geometry repeatedly asked in JEE Advanced previous year question papers. Therefore, revising these concepts is necessary for performing well in the exam.
Must Read Articles:
- Download JEE Advanced Question Last 10 year PYQ for Free
- Download JEE 2024 Paper with Detailed Solutions
Listed below the most repeated questions JEE Advanced Previous Year Questions (PYQs) for Ellipse along with detailed solutions:
Question 1:
Consider the ellipse
Let H(α,0),0< α<2 , be a point. A straight line drawn through H parallel to y-axis crosses the ellipse and its auxiliary circle at points E and F respectively, in the first quadrant. The tangents to the ellipse at the point E intersects the positive x-axis at a point G. Suppose the straight line joining F and the origin makes an angle ϕ with the positive x-axis.
| List-I | List-II | ||
|---|---|---|---|
| (I) | If Φ=π4Φ=4π, then the area of the triangle FGH is | P | (3−1)488(3−1)4 |
| (II) | If Φ=π3Φ=3π, then the area of the triangle FGH is | Q | 1 |
| (III) | If Φ=π6Φ=6π, then the area of the triangle FGH is | R | 3443 |
| (IV) | If Φ=π12Φ=12π, then the area of the triangle FGH is | S | 123231 |
| T | 332233 | ||
Question 2:
The area of the quadrilateral formed by the tangents at the end points of latusrectum
Question 3:
A normal with slope 1/root 6 is drawn from the point (0, -α) to the parabola x2 = -4αy, where a > 0. Let L be the line passing through (0, -α) and parallel to the directrix of the parabola. Suppose that L intersects the parabola at two points A and B. Let r denote the length of the latus rectum and s denote the square of the length of the line segment AB. If r : s = 1 : 16 then the value of 24a is __________.
Question 4:
Question 5:
Question 6:
The locus of the foot of perpendicular drawn from the centre of the ellipse
x2+3y2=6 on any tangent to it is
- (x2+y2)2=6x2+2y2
- (x2+y2)2=6x2−2y2
- (x2−y2)2=6x2+2y2
- (x2−y2)2=6x2−2y2
Question 7:
Question 8:
An ellipse intersects the hyperbola 2x2−2y2=1 orthogonally. The eccentricity of the ellipse is reciprocal to th a t of the hyperbola. If the axes of the ellipse are along the coordinate axes, then
- (a) equation of ellipse is x2+2y2=2
- (b) the foci of ellipse are (±1, 0)
- (c) equation of ellipse is x2+2y2=4
- (d) the foci of ellipse are (±2,0)
JEE Advanced Exam Pattern 2025
- Mode of the exam: The examination 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 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 the ellipse important for JEE Advanced?
Yes, ellipse is an important topic for JEE Advanced under the Coordinate geometry and questions inter-related with hyperbolas and equations of ellipse are frequently asked in the exam. Mastering this topic of geometry will fetch you good marks.
Q2. Who is the father of coordinate geometry?
Rene Descartes is considered the father of Coordinate Geometry. He introduced the concept of geometric shapes using algebraic equations. He combined algebra and geometry making it simple to solve complex geometric problems using algebraic methods.
Q3. Which is the most scoring subject in JEE Advanced?
Most scoring subject in JEE Advanced may differ from person to person based on strengths, but most of the time Mathematics is one of the most scoring subjects. Topics of Probability like conditional probability, Definite integration and 3D geometry have heavy weightage. These are all calculation-based concepts, so with frequent practice, it is easy for students to get good marks.
Q4. 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.
Comments