Let P be a parabola with vertex (2,3) and directrix 2x+y=6. Let an ellipse E: \;x²/a²+\;y²/b²=1, ab 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 [31-Jan-2024 Shift 2]

Question

Let P be a parabola with vertex (2,3) and directrix 2x+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 [31-Jan-2024 Shift 2]

Examsnet · Accepted Answer

Correct Answer is : 65625\;656/2525656​

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