JEE Main 2024 Mathematics question
Let A(α, 0) and B(0, β) be the points on the line 5x + 7y = 50. Let the point P divide the line segment AB internally in the ratio 7 : 3. Let 3x − 25 = 0 be a directrix of the ellipse E : x²/a² + y²/b² = 1 and the corresponding focus be S. If from S, the perpendicular on the x-axis passes through P, then the length of the latus rectum of E is equal to
Answer: (A)
Solution
On 5x + 7y = 50, A = (10, 0) and B = (0, 50/7). P divides AB in the ratio 7 : 3: P = ((0 + 3 × 10)/10, (7 × 50/7 + 0)/10) = (3, 5). The perpendicular from S to the x-axis
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