Q. 2 C5.0( 1 Vote )

Find the equation

Answer :

Given: Equation of directrix of a hyperbola is 2x + y – 1 = 0. Focus of hyperbola is (1, 1) and eccentricity (e) =


To find: equation of hyperbola


Let M be the point on directrix and P(x, y) be any point of hyperbola


Formula used:



where e is eccentricity, PM is perpendicular from any point P on hyperbola to the directrix


Therefore,




Squaring both sides:




{ (a – b)2 = a2 + b2 + 2ab &


(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac}


5{x2 + 1 – 2x + y2 + 1 – 2y} = 3{4x2 + y2+ 1 + 4xy – 2y – 4x}


5x2 + 5 – 10x + 5y2 + 5 – 10y = 12x2 + 3y2 + 3 + 12xy – 6y – 12x


5x2 + 5 – 10x + 5y2 + 5 – 10y – 12x2 – 3y2 – 3 – 12xy + 6y + 12x = 0


– 7x2 + 2y2 + 2x – 4y – 12xy + 7 = 0


7x2 – 2y2 – 2x + 4y + 12xy – 7 = 0


This is the required equation of hyperbola.



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