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

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

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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