Ellipse JEE Main PYQs PDF, 2020–2026

Ellipse questions per year

Topic-wise weightage by year

How many Ellipse questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Swipe the table sideways for older years.

Newest questions (2026)

The 12 newest of the 15 JEE Main 2026 Ellipse questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Parametric Form

   Let $\frac{x^{2}}{f(a^{2}+7a+3)}+\frac{y^{2}}{f(3a+15)}=1$ represent an ellipse with major axis along $y$-axis, where $f$ is a strictly decreasing positive function on ${\mathbf{R}}$. If the set of all possible values of $a$ is ${\mathbf{R}}-[\alpha,\beta]$, then $\alpha^{2}+\beta^{2}$ is equal to :

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2. JEE Main 2026 · 6 Apr · Shift 2 · Focal Chord

   Let $x=9$ be a directrix of an ellipse E , whose centre is at the origin and eccentricity is $\frac{1}{3}$. Let ${\mathrm{P}}(\alpha,0)$, $\alpha>0$, be a focus of E and AB be a chord passing through P . Then the locus of the mid point of AB is :

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3. JEE Main 2026 · 5 Apr · Shift 1 · Parametric Form

   Let a focus of the ellipse ${\mathrm{E}}:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ be ${\mathrm{S}}(4,0)$ and its eccentricity be $\frac{4}{5}$. If the point ${\mathrm{P}}(3,\alpha)$ lies on E and O is the origin, then the area of $\triangle {\mathrm{POS}}$ is equal to:

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4. JEE Main 2026 · 4 Apr · Shift 1 · Parametric Form

   Consider the parabola ${\mathrm{P}}:y^{2}=4kx$ and the ellipse ${\mathrm{E}}:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$. Let the line segment joining the points of intersection of P and E , be their latus rectums. If the eccentricity of E is $e$, then $e^{2}+2\sqrt{2}$ is equal to $\_\_\_\_$ .

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5. JEE Main 2026 · 4 Apr · Shift 2 · Parametric Form

   Let ${\mathrm{P}}(3\cos \alpha,2\sin \alpha),\alpha\neq 0$, be a point on the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1,{\mathrm{Q}}$ be a point on the circle $x^{2}+y^{2}-14x-14y+82=0$ and R be a point on the line $x+y=5$ such that the centroid of the triangle PQR is $\left(2+\cos \alpha,3+\frac{2}{3}\sin \alpha\right)$. Then the sum of the ordinates of all possible points R is:

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6. JEE Main 2026 · 2 Apr · Shift 1 · Parametric Form

   Let an ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$, $a<b$, pass through the point (4, 3) and have eccentricity $\frac{\sqrt{5}}{3}$.

   Then the length of its latus rectum is :

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7. JEE Main 2026 · 2 Apr · Shift 2 · Standard Equation

   Let A be the point (3, 0) and circles with variable diameter AB touch the circle $x^{2}+y^{2}=36$ internally. Let the curve C be the locus of the point B. If the eccentricity of C is $e$, then $72e^{2}$ is equal to ________.

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8. JEE Main 2026 · 28 Jan · Shift 2 · Parametric Form

   An ellipse has its center at $(1,-2)$, one focus at $(3,-2)$ and one vertex at $(5,-2)$. Then the length of its latus rectum is :

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9. JEE Main 2026 · 24 Jan · Shift 2 · Parametric Form

   Let $(h,k)$ lie on the circle ${\mathrm{C}}:x^{2}+y^{2}=4$ and the point $(2h+1,3k+2)$ lie on an ellipse with eccentricity $e$. Then the value of $\frac{5}{e^{2}}$ is equal to $\_\_\_\_$ .

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10. JEE Main 2026 · 24 Jan · Shift 2 · Parametric Form

    Let the length of the latus rectum of an ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1,(a>b)$, be 30 . If its eccentricity is the maximum value of the function $f(t)=-\frac{3}{4}+2t-t^{2}$, then $\left(a^{2}+b^{2}\right)$ is equal to

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11. JEE Main 2026 · 24 Jan · Shift 1 · Parametric Form

    Let each of the two ellipses ${\mathrm{E}}_{1}:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1,(a>b)$ and ${\mathrm{E}}_{2}:\frac{x^{2}}{{\ \mathrm{A}}^{2}}+\frac{y^{2}}{{\ \mathrm{B}}^{2}}=1,({\ \mathrm{A}}<{\mathrm{B}})$ have eccentricity $\frac{4}{5}$. Let the lengths of the latus recta of ${\mathrm{E}}_{1}$ and ${\mathrm{E}}_{2}$ be $l_{1}$ and $l_{2}$, respectively, such that $2l_{1}^{2}=9l_{2}$. If the distance between the foci of $E_{1}$ is 8 , then the distance between the foci of $E_{2}$ is

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12. JEE Main 2026 · 23 Jan · Shift 2 · Standard Equation

    If the points of intersection of the ellipses $x^{2}+2y^{2}-6x-12y+23=0$ and
    
    $4x^{2}+2y^{2}-20x-12y+35=0$ lie on a circle of radius $r$ and centre $(a,b)$, then the
    
    value of $ab+18r^{2}$ is :

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JEE Main PYQs by year: 2026 · 2025 · 2024 · 2023 · 2022 · 2021 · 2020