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Find the equations of the tangents to the hyperbola 9x^{2}-16y^{2}=1\, drawn parallel to to the line 9x+8y=10\,

Any line parallel to the given line can be written as 9x+8y+k=0\,

From this l=9,m=8,n=k\,

From the given hyperbola a^{2}={\frac  {10}{9}},b^{2}={\frac  {10}{8}}\,

The condition of tangency is {\frac  {10}{9}}(81)-{\frac  {10}{8}}(64)=k^{2}\,

k^{2}=90-80,k=\pm {\sqrt  {10}}\,

Therefore,the equations of tangents are 9x+8y\pm {\sqrt  {10}}=0\,

Main Page:Geometry:Hyperbola