Geo5.1.16

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Find the value of p if the line x+y+2=0\, touches the parabola y^{2}=px\,

Given parabola is y^{2}=px\, and the touching line or tangent is x+y+2=0\,

From the given line

l=1,m=1,n=2\,

The condition for a line to be tangent to a parabola is

ln=am^{2}\,

(1)(2)={\frac  {p}{4}}(1)^{2}\,

p=8\,


Main Page:Geometry:The Parabola