Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main 20253 AprilEvening Shift

Exam: JEE Main
Year: 2025
Date: 3 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Ellipse

JEE Main 2025 · 3 April · Evening Shift · Mathematics · Ellipse

Let C be the circle of minimum area enclosing the ellipse E:...

Let

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 foci

( \pm 2,0)

. Let PQR be a variable triangle, whose vertex

P

is on the circle

C

and the side

Q R

of length 29 is parallel to the major axis of

E

and contains the point of intersection of

E

with the negative

y

-axis. Then the maximum area of the triangle PQR is :

Options

A $6(3+\sqrt{2})$
B $8(3+\sqrt{2})$
C $62+\sqrt{3}$
D $82+\sqrt{3}$

Correct answer

D. $82+\sqrt{3}$

Step-by-step solution

Area of

\triangle P Q R

\begin{aligned}& =\frac{1}{2}(2 a)(a \sin \theta+b) \\ & \therefore \text{ maximum area }=a(a+b) \\ & \quad=4(4+2 \sqrt{3})=8(2+\sqrt{3})\end{aligned}

$$

Practice Ellipse on Quantrex Academy →

More from Ellipse

Consider the ellipse E given by (x^2)/(18) + (y^2)/(12) = 1 . Let H be the hyperbola… JEE Advanced 2026 Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: Let… JEE Advanced 2026 Let (x^2)/(f(a^2+7a+3)) + (y^2)/(f(3a+15)) = 1 represent an ellipse with major axis along… JEE Main 2026 The eccentricity of an ellipse E with centre at the origin O is 3 2 and its directrices… JEE Main 2026 Let x = 9 be a directrix of an ellipse E , whose centre is at the origin and eccentricity… JEE Main 2026 Let a focus of the ellipse E: (x^2)/(a^2) + (y^2)/(b^2) = 1 be S(4, 0) and its… JEE Main 2026 Let A be the point (3, 0) and circles with variable diameter AB touch the circle x^2 +… JEE Main 2026 Let an ellipse (x^2)/(a^2) + (y^2)/(b^2) = 1 , a < b , pass through the point (4, 3) and… JEE Main 2026 An ellipse has its center at (1,-2) , one focus at (3,-2) and one vertex at (5,-2) . Then… JEE Main 2026 Let the ellipse E: x^ 2 144 + y^ 2 169 =1 and the hyperbola H: x^ 2 16 - y^ 2 λ^ 2 =-1… JEE Main 2026 Let the length of the latus rectum of an ellipse x^ 2 a^ 2 + y^ 2 b^ 2 =1,(a>b) , be 30.… JEE Main 2026 Let (h, k) lie on the circle C: x^ 2 +y^ 2 =4 and the point (2 h+1,3 k+2) lie on an… JEE Main 2026 Let each of the two ellipses E_ 1 : x^ 2 a^ 2 + y^ 2 b^ 2 =1,(a>b) and E_ 2 : x^ 2 ~A^ 2… JEE Main 2026 Let the line y-x=1 intersect the ellipse x^ 2 2 + y^ 2 1 =1 at the points A and B. Then… JEE Main 2026 Let S and S^ be the foci of the ellipse x^ 2 25 + y^ 2 9 =1 and P(α, β) be a point on the… JEE Main 2026 If the line α x+4 y= 7 , where α ∈ R , touches the ellipse 3 x^ 2 +4 y^ 2 =1 at the point… JEE Main 2026 Full Ellipse list Ellipse JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs