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Find the equations to the tangents to the hyperbola 3x^{2}-y^{2}=3\, which are perpendicular to x+3y=2\,

From the given hyperbola a^{2}=1,b^{2}=3\,

Equation to any line perpendicular to x+3y-2=0\, is 3x-y+k=0\,

This is a tangent to the given hyperbola,hence the condition of tangency is

1(3)^{2}-3(-1)^{2}=k^{2},k^{2}=6,k=\pm {\sqrt  {6}}\,

Therefore,the required tangents are 3x-y\pm {\sqrt  {6}}=0\,

Main Page:Geometry:Hyperbola