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Circle question

2025 · 23 Jan · Shift 1 · Q49

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PYQ Library
JEE Main
Mathematics
Circle
2025 · 23 Jan · Shift 1 · Q49

Circle question

2025 · 23 Jan · Shift 1 · Q49

JEE MainMathematicsCircleNumerical+4 / −1

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

\frac{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

\underline{\hspace{2cm}}

.

Numerical answer

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