Geo5.3.1

From Example Problems
Jump to: navigation, search

Write down the equation to the hyperbola whose focus is (4,0)\,,directrix is the line 4x-9=0\, and eccentricity is 4/3.

Given S=(4,0),l\equiv 4x-9=0,e={\frac  {4}{3}}\,

The equation to hyperbola is

(x-4)^{2}+(y-0)^{2}=[{\frac  {4}{3}}]^{2}[{\frac  {4x-9}{{\sqrt  {16}}}}]^{2}\,

x^{2}+y^{2}-8x+16={\frac  {16x^{2}+81-72x}{9}}\,

9x^{2}+9y^{2}-72x+144=16x^{2}-72x+81\,

7x^{2}-9y^{2}=63\,


Main Page:Geometry:Hyperbola