JEE Main Maths · Conic Sections

Ellipse Eccentricity in JEE Main

Name: Ellipse Eccentricity: JEE Main previous year questions
Creator: Lumi

Ellipse Eccentricity (Maths, Conic Sections) came 20 times in 19 of the 42 JEE Main shifts Lumi analysed, across 10 distinct ideas. 16 of them came in 2024–26; it was last asked in 2026.

Questions: 20; in 19 shifts
Ideas asked: 10; 5 asked more than once
Numerical answer: 2; 10% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 3Medium 12Hard 5

Format

Single correct18 Q
Numerical value2 Q

Ideas inside the topic

10 ideas

Length of Latus Rectum5 Q
Eccentricity calculation3 Q
Focal distance property3 Q
Coordinates of foci2 Q
Product of Focal Distances2 Q
Center to Focus Distance1 Q
Equations of directrices1 Q
Distance Between Foci1 Q
Eccentricity when Normal at LR End Passes Through Minor Axis1 Q
Vertical Ellipse Latus Rectum1 Q

Where it sits

Part of Conic Sections, which had 116 questions in all. Ellipse Eccentricity accounts for 17% of them. In Lumi's JEE taxonomy it belongs to Coordinate Geometry.

Some questions sit in other chapters too: Complex Numbers and Quadratic Equations.

Every question

All 20 Ellipse Eccentricity questions

Newest first, each with its options and official answer.

2 Apr 2026, Shift 1 · Q10Let an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , $a<b$ , pass through the point $(4, 3)$ and have eccentricity $\frac{\sqrt5}{3}$ . Then…MediumSingle correct
4 Apr 2026, Shift 1 · Q22Consider the parabola $P: y^2=4kx$ and the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ . Let the line segment joining the points of…MediumNumerical value
5 Apr 2026, Shift 1 · Q9Let a focus of the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ be $S(4, 0)$ and its eccentricity be $\frac{4}{5}$ . If the point…EasySingle correct
8 Apr 2026, Shift 2 · Q2The number of values of $z \in \mathbb{C}$ , satisfying the equations $|z - (4 + 8i)| = \sqrt{10}$ and…HardSingle correct
2 Apr 2025, Shift 1 · Q4If S and S' are the foci of the ellipse $\frac{x^2}{18}+\frac{y^2}{9}=1$ and P be a point on the ellipse, then…MediumSingle correct
2 Apr 2025, Shift 2 · Q12If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the…EasySingle correct
3 Apr 2025, Shift 2 · Q12Let $C$ be the circle of minimum area enclosing the ellipse $E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with eccentricity $\frac{1}{2}$ and…HardSingle correct
4 Apr 2025, Shift 2 · Q11The centre of a circle C is at the centre of the ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , $a>b$ . Let C pass through the foci $F_1$ …HardSingle correct
7 Apr 2025, Shift 2 · Q12Let the length of a latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ be 10. If its eccentricity is the minimum value of the…MediumSingle correct
7 Apr 2025, Shift 2 · Q13Let $e_1$ and $e_2$ be the eccentricities of the ellipse $\frac{x^2}{b^2}+\frac{y^2}{25}=1$ and the hyperbola…MediumSingle correct
8 Apr 2025, Shift 2 · Q12Let the ellipse $3x^2 + py^2 = 4$ pass through the centre $C$ of the circle $x^2 + y^2 - 2x - 4y - 11 = 0$ of radius $r$ . Let $f_1, f_2$ …MediumSingle correct
9 Apr 2024, Shift 1 · Q12Let $f(x)=x^2+9$ , $g(x)=\frac{x}{x-9}$ and $a=f\circ g(10)$ , $b=g\circ f(3)$ . If $e$ and $l$ denote the eccentricity and the length of the…EasySingle correct
9 Apr 2024, Shift 2 · Q15Let the foci of a hyperbola $H$ coincide with the foci of the ellipse $E:\frac{(x-1)^2}{100}+\frac{(y-1)^2}{75}=1$ and the eccentricity of…MediumSingle correct
30 Jan 2024, Shift 2 · Q14Let $A(\alpha, 0)$ and $B(0, \beta)$ be the points on the line $5x + 7y = 50$ . Let the point $P$ divide the line segment $AB$ internally…MediumSingle correct
31 Jan 2024, Shift 1 · Q28Let the foci and length of the latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b$ be $(\pm5,0)$ and $\sqrt{50}$ ,…MediumNumerical value
31 Jan 2024, Shift 2 · Q14Let $P$ be a parabola with vertex $(2,3)$ and directrix $2x+y=6$ . Let an ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\ a>b$ , of…HardSingle correct
3 Aug 2021, Shift 2 · Q74If an ellipse passes through the point $(4, 1)$ and has foci at $(\pm3, 0)$ , then its eccentricity isMediumSingle correct
25 Jul 2021, Shift 1 · Q61Let an ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ , $a^2>b^2$ , passes through $\left(\sqrt{\frac{3}{2}},1\right)$ and has eccentricity…HardSingle correct
9 Jan 2020, Shift 2 · Q65The length of the minor axis (along $y$ -axis) of an ellipse in the standard form is $\frac{4}{\sqrt3}$ . If this ellipse touches the line,…MediumSingle correct
6 Sep 2020, Shift 2 · Q66If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity e of the…MediumSingle correct