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Ellipse question

2025 · 3 Apr · Shift 2 · Q30

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PYQ Library
JEE Main
Mathematics
Ellipse
2025 · 3 Apr · Shift 2 · Q30

Ellipse question

2025 · 3 Apr · Shift 2 · Q30

JEE MainMathematicsEllipseMCQ+4 / −1

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

P Q R

be a variable triangle, whose vertex

P

is on the circle

C

and the side

Q R

of length

2 a

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

P Q R

is :

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

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