Let circle C be the image of x^2+y^2-2 x+4 y-4=0 in the line 2 x-3 y+5=0 and A be the point on C such that O A is parallel to x-axis and A lies on the righthand side of the centre O of C. If B(\alpha, \beta), with \beta< 4, lies on C such that the length of the {\arc} A B is (1 \/ 6)^{\text{th }} of the perimeter of C, then \beta-\sqrt{3} \alpha is equal to [24 Jan 2025 Shift 1]

JEE Main 24 Jan 2025 Shift 1 Paper

Section: Mathematics

Question : 14 of 75

Marks: +1, -0

Let circle C be the image of x2+y2−2x+4y−4=0 in the line 2x−3y+5=0 and A be the point on C such that OA is parallel to x-axis and A lies on the righthand side of the centre O of C. If B(α,β), with β<4, lies on C such that the length of the arc‌A‌B is (1∕6)‌th ‌ of the perimeter of C, then β−√3α is equal to

[24 Jan 2025 Shift 1]

4
3
4−√3
3+√3

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