JEE Main 2024 Mathematics question
Let the line 2x + 3y − k = 0, k > 0, intersect the x-axis and y-axis at the points A and B, respectively. If the equation of the circle having the line segment AB as a diameter is x² + y² − 3x − 2y = 0 and the length of the latus rectum of the ellipse x² + 9y² = k² is , where m and n are coprime, then 2m + n is equal to
Answer: (B)
Solution
A = (k/2, 0) lies on the circle, so k/2 = 3 and k = 6. The ellipse x²/36 +
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