Geo5.3.15

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Find the equations of tangents to the hyperbola 4x^{2}-3y^{2}=24\, which make an angle of 60 degrees with X-axis.

Equation of the tangents is y=mx\pm {\sqrt  {a^{2}m^{2}-b^{2}}}\,

Given hyperbola is {\frac  {x^{2}}{6}}-{\frac  {y^{2}}{8}}=1\,

a^{2}=6,b^{2}=8\,

Slope of the line is m=\tan 60={\sqrt  {3}}\,

Therefore,the equations of tangents are y={\sqrt  {3}}x\pm {\sqrt  {6(3)-8}}\,

y={\sqrt  {3}}x\pm {\sqrt  {10}}\,


Main Page:Geometry:Hyperbola