How to find an equation of the parabola with focus (0,0) and directrix x + y = 4

How to find an equation of the parabola with focus (0,0) and directrix x + y = 4

Interesting problem - given that the directrix is at a 45 degree angle to the x and y axes this adds a twist to the "typical" conic section homework problem. One way to attack this is by perfroming a transformation from (x,y) coordinates to a new set of coordinates - call them (s,t) - that are rotated 45 degrees from (x,y). This (s,t) coordinate system will be compatible with the standard parabola formulas. Then you would perform a transformation back to the (x,y) coordinate system. It would look like the figure below. But before going any further - are you sure you copied this problem exactly as stated in the text?