parabola as a locus (1 Viewer)

[blacktown_]

the focal chord that cuts the parabola x^2 = -6y at (6,-6) cuts the parabola again at X. find the coordinates of X

 

[michaeljennings]

Start off by finding the equation of the focal chord using the focus and (6,-6) to find the gradient and then use point gradient formula to find the equation of the line.
Solve simultaneously for the line and the parabola you should get two answers, one being x=6 and the other being the x-coordinate of X

 

[blacktown_]

Thankyou very much! you're awesome