Geo5.3.13

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Find the equations of the tangents to the hyperbola 3x^{2}-4y^{2}=12\, which make equal intercepts on the axes.

Given hyperbola {\frac  {x^{2}}{4}}-{\frac  {y^{2}}{3}}=1\,

Let the equations to the lines with equal length of intercepts on the axes be x\pm y=\pm k\,

This is a tangent to the given hyperbola, hence

4(1)-3(1)=k^{2},k=1\,

Therefore,tangent lines are x\pm y=\pm 1\,


Main Page:Geometry:Hyperbola