Geo5.3.19

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Find the equation of the normal at (1,0)on the hyperbola x^{2}-4y^{2}=1\,

Equation to the normal at (x_{1},y_{1})\, on {\frac  {x^{2}}{a^{2}}}-{\frac  {y^{2}}{b^{2}}}=1\, is {\frac  {a^{2}x}{x_{1}}}+{\frac  {b^{2}y}{y_{1}}}=a^{2}+b^{2}\,

a^{2}xy_{1}+b^{2}x_{1}y=(a^{2}+b^{2})x_{1}y_{1}\,

Therefore,the equation of the normal at (1,0) is 1(x)(0)+{\frac  {1}{4}}(1)(y)=[1+{\frac  {1}{4}}](1)(0)\,

y=0\,


Main Page:Geometry:Hyperbola