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Show that the line x+ 2y + 8 = 0 is tangent to the parabola y2 = 8x. Hence find the point of contact - Mathematics and Statistics

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Show that the line x+ 2y + 8 = 0 is tangent to the parabola y2 = 8x. Hence find the point of contact

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Solution

Given line is

`2y = – x – 8`

`y=-1/2x-4`

`therefore m=-1/2 , c=-4`

equation of Parabola

`y^2=8x`

`a=2`

`therefore a/m=2/(-1/2)=-4=c`

Hence x +2y +8 = 0 is tangent to the Parabola y2 = 8x

Point tocontact `=(a/m^2,(2a)/m)`

`a/m^2=2/(1/4)=8`

`(2a)/m=(2xx2)/(-1/2)=-8`

Point of contat (8, –8)

Concept: Conics - Tangents and normals - equations of tangent and normal at a point
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