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Help? (1 Viewer)

Thread starter Vespers
Start date Oct 25, 2009

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Vespers

New Member

#1

i) Show that for all values of m, the line y = mx - 3m^2 touches the parabola x^2 = 12y. Can someone explain this one to me? I know how to do it, I just don't understand why... Thanks.

untouchablecuz

Active Member

#2

$\text{Solve simultaneously,}\\12(mx-3m^2)=x^2\\(1)x^2+(-12m)x+(36m^2)=0\\\bigtriangleup =(-12m)^2-4(1)(36m^2)=144m^2-144m^2=0\\\text{This means that there is only one distinct solution to this equation}\\\text{Since the number of solutions represents the number of points of intersection,}\\\text{There is only one point of intersection}\\\therefore y=mx-3m^2 \text{ touches }x^2=12y \text{ for all values of }m$

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