Let the equation of two diameters of a circle x²+y²-2 x+2 f y+1=0 be 2 p x-y=1 and 2 x+p y=4 p. Then the slope m (0, ∞) of the tangent to the hyperbola 3 x²-y²=3 passing through the centre of the circle is equal to _ _ _ _ _ _ _ _.

Coordinate Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jul, Morning shift · Q35

JEE Main 202225 Jul, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

Let the equation of two diameters of a circle

x^{2}+y^{2}-2 x+2 f y+1=0

2 p x-y=1

and

2 x+p y=4 p

. Then the slope m

\in

(0, \infty)

of the tangent to the hyperbola

3 x^{2}-y^{2}=3

passing through the centre of the circle is equal to _______________.

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