The equation of the hyperbola whose asymptotes are the lines 3 x+4 y-2=0 , 2 x+y+1=0 and which passes through the point (1,1) is

Step-by-step solution

Equation to the asymptotes are given as aligned 3 x+4 y-2 & =0 2 x+y+1 & =0 aligned and Eqs.(i) and (ii) may be given by (3 x+4 y-2)(2 x+y+1)=0 As, the equation to the hyperbola will differ from Eq. (iii) only by a constant, it may be given by (3 x+4 y-2(2 x+y+1)= (where is a constant) (1,1) lies on the curve given by Eq. (iv), we have aligned & & (3+4-2)(2+1+1) & = & & (5)(4)= & =20 aligned Hence, the equation of the hyperbola will be aligned & (3 x+4 y-2)(2 x+y+1)=20 & 6 x^2+3 x y+3 x+8 x y+4 y^2 & +4 y-4 x-2 y-2