Geo5.2.46

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Find the point of contact of the tangent line 4x+y-7=0\, to the ellipse x^{2}+3y^{2}=3\,

The given tangent is 4x+y-7=0\,

The elipse is x^{2}+3y^{2}=3\,

From the two equations

l=4,m=1,n=-7,a^{2}=3,b^{2}=1\,

The point of contact is \left({\frac  {-a^{2}l}{n}},{\frac  {-b^{2}m}{n}}\right)\,

\left({\frac  {(-3)(4)}{-7}},{\frac  {(-1)(1)}{-7}}\right)\,

\left({\frac  {12}{7}},{\frac  {1}{7}}\right)\,


Main Page:Geometry:The Ellipse