Need help with a parametrics question (1 Viewer)

[impulsebro89]

Hi everyone!

Will you please help me with this question:

The points A (−6, -9) and B(u,v) lie on the parabola x^2 =-4ay such that AB is a normal to the parabola at B.
(i) Find the value of a.
(ii)Given the roots of x^3 − 28x + 48 = 0 are −6, 2, 4, find the coordinates of B.

I can't seem to get part (ii).

Help please! Thanks

 

[fan96]

Re: Interesting parametrics question!

i)

Using the general equation of the parabola



and the given point , we can deduce .

ii)

Let be given by



The cartesian equation of the normal to the parabola is

.

Using the coordinates of to substitute in for ,



Which gives the equation of the normal to the parabola at the point .

Because we require to be on the normal, we can substitute into the equation and solve for .

After substitution and simplfication you will get the equation given to you in ii).