Geo5.1.19

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Show that the line x-y+2=0\, is a tangent to y^{2}=8x\,.Find the point of contact.

Given line and parabola are

x-y+2=0,y^{2}=8x\,

The condition for the tangent is

ln=am^{2}\,

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

Hence the line is tangent to the parabola.

The point of contact is

\left({\frac  {a}{m^{2}}},{\frac  {2a}{m}}\right)\,

\left({\frac  {2}{1}},{\frac  {4}{-1}}\right)\,

\left(2,-4\right)\,


Main Page:Geometry:The Parabola