Find the equation of the hyperbola whose directrix is 2x y 1 focus 1 2 and eccentricity radic ...........

Mathematics (NDA) Coordinate Geometry

Find the equation of the hyperbola whose directrix is 2x + y = 1, focus (1, 2), and eccentricity √3?

x²-2y²+12xy-2x+14y-22=0

7x²-2y²+12xy-2x+14y-22=0

7x²-y²+12xy-2x+14y+22=0

7x²-2y²+xy-2x+14y-22=0

Let P(x, y) be any point on the hyperbola and PM is perpendicular from P on the directrix. Then by definition SP = e PM

(SP)² = e² (PM)²

(x-1)² +(y-2)²=3 (2x+y-1/√4+1)

5(x+y-2x-4y+5)=3(4x²+y²+1+4xy-2y-4x)

7x²-2y²+12xy-2x+14y-22=0

Hyperbola 7x²-2y²+12xy-2x+14y-22=0

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