JEE Main 2026 · MathsMultiple choiceSingle correctEasyMulti-step

JEE Main 5 April 2026, Shift 1, Maths Q9

Question 9 of 75 in this shift, Maths question 9 of 25, Section A.

Let a focus of the ellipse

E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1

S(4, 0)

and its eccentricity be

\frac{4}{5}

. If the point

P(3, \alpha)

lies on E and O is the origin, then the area of

\Delta POS

is equal to:

(1)12/5
(2)14/5
(3)24/5Official answer
(4)48/5

Official answer

Option 3

NTA final key.

Chapter: Conic Sections
Topic: Ellipse Eccentricity
Idea tested: Eccentricity calculation

Same idea in other shifts

Asked 3× in all

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

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.