From Example Problems
Jump to: navigation, search

The asymptotes of the hyperbola are parallel to the lines 2x+3y=0,3x+2y=0\,. Its centre is at (1,2)\, and passes thro' the point (5,3)\,.Find its equation.

The equations of the asymptotes are 2x+3y+k=0,3x+2y+l=0\,

The asymptotes pass through the centre (1,2)\,


Therefore,the asymptotes are 2x+3y-8=0,3x+2y-7=0\,

The combined equation of the asymptotes is (2x+3y-8)(3x+2y-7)=0\,

Hence the equation to the hyperbola is (2x+3y-8)(3x+2y-7)+\lambda =0\,

Since the hyperbola passes through (5,3)\,

(10+9-8)(15+6-7)+\lambda =0,\lambda =-154\,

Hence the equation of hyperbola is (2x+3y-8)(3x+2y-7)-154=0\,


Main Page:Geometry:Hyperbola