Let the circle C touch the line x-y+1=0, have the centre on the positive x-axis, and cut off a chord of length {4}/{\sqrt{13}} along the line -3 x+2 y=1. Let H be the hyperbola \frac{x^2}{\alpha^2}-\frac{y^2}{\beta^2}=1, whose one of the foci is the centre of C and the length of the transverse axis is the diameter of C. Then 2 \alpha^2+3 \beta^2 is equal to________ [23 Jan 2025 Shift 1]

Circles Part 2

Section: Mathematics

Question : 16 of 78

Marks: +1, -0

Let the circle C touch the line x−y+1=0, have the centre on the positive x-axis, and cut off a chord of length ‌

√13

along the line −3x+2y=1. Let H be the hyperbola ‌

α2

−‌

β2

=1, whose one of the foci is the centre of C and the length of the transverse axis is the diameter of C. Then 2α2+3β2 is equal to________

[23 Jan 2025 Shift 1]

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