Focal Length and Parabola Question (1 Viewer)

[Redyapper]

Hi,

I need some help with this question please
The focal chord that cuts the parabola x^2 = -6y at (6, -6) cuts the parabola again at point X. Find the co-ordinates of X.

I'm clueless!

Thanks!

 

[qrpw]

The focus is (0,-6/4), from the definition of a parabola. Now find the equation of the line joining the focus and (6,-6), you should get y + 1.5 = -3/4 x.

Now solve this simultaneously with the parabola to find points of intersection, and you'll get two of them- one will be (6,-6) and the other one will be X. Try and do it yourself without looking at any answers.