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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 : 2 2 2 2 b y a x + = 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

1. 5 32
2. 3 25
3. 9 32
4. 9 25

Correct answer: 5 32

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