sloving parabola equations

[INAM KHAN]

how can i slove equation of parabola when focus and Latusrectom are given.

[imatfaal]

I don't think you can uniquely as there will be two symmetric parabolas with those in common

 

You can find out the vertex from the latus rectum and the focus, as you know that the latus rectum is 4 times the distance of the focus to the vertex

 

You then plug into equation (x-h)^2 = +/-4p (y-k)

 

where p is the distance from focus to vertex and (h,k) are the coordinate of the vertex. The +- gives you two different parabolas one the flipped over version of the other