Geo5.3.14

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Find the value of k if the line 3x-y=k\, is a tangent to 3x^{2}-y^{2}=3\,

The given hyperbola is {\frac  {x^{2}}{1}}-{\frac  {y^{2}}{3}}=1\,

a^{2}=1,b^{2}=3\,

Given line is 3x-y-k=0\,

From the line l=3,m=-1,n=k\,

The condition of tangency is a^{2}l^{2}-b^{2}m^{2}=n^{2}\,

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

k^{2}=12,k=\pm 2{\sqrt  {3}}\,


Main Page:Geometry:Hyperbola