Let P be a parabola with vertex (2,3) and directrix 2 x+y=6. Let an ellipse E: (x²)/(a²)+(y²)/(b²)=1, a>b, of eccentricity 1/(√(2)) pass through the focus of the parabola P. Then, the square of the length of the latus rectum of E, is

Coordinate Geometry: JEE Main 2024 Mathematics question

JEE Main 2024 · 31 Jan, Evening shift · Q3768

JEE Main 202431 Jan, Evening shiftMathematicsHardCoordinate Geometry478× since 2002

Let

P

be a parabola with vertex

(2,3)

and directrix

2 x+y=6

. Let an ellipse

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

, of eccentricity

\frac{1}{\sqrt{2}}

pass through the focus of the parabola

P

. Then, the square of the length of the latus rectum of

E

, is