Parabola Question?? (1 Viewer)

[kenk]

Can anyone help me out with this question.. I've got it in an assessment and I have no clue..

a)Show that for all values of m, the line y=mx-3m^2 touches the parabola x^2=12y
b)Find the values of m for which this line passes through the points(5,2)

Any help at all would be muchly appreciated..

 

[Riviet]

For b, substitute x=5, y=2 into y=mx-3m² and solve for m.

 

[Mountain.Dew]

For a, do simultaenous equations, get an equation in terms of x. then, find the discriminant, and you shall see that it will become zero. therefore, for all values of m, the line touches the parabola once.

 

[pLuvia]

For a sub y=mx-3m² into the equation then make it into a quadratic. Using the discriminant solve for m. As you know it touches the graph then the discriminant = 0

Hope that helped

Edit: M.D too quick

 

[kenk]

Thanks heaps for that!