Finding equation of parabola (1 Viewer)

[HSC2014]

Q: Find the equation of the parabola whose focus is (-3,-1) and directrix 3x - 2y = 5

As far as I can tell this is a slanted parabola, since directrix is slanted?

If I let (x,y) be a point on the parabola then
(x+3)^2 + (y+1)^2 = (3x - 2y -5)^2/ 13 (distance of (x,y) from focus and directrix is equal; using distance formula and perpendicular distance formula)

I don't know what to do from here Is this the complete answer or should I "simplify" further (it doesn't simplify elegantly)

 

[themoonspretty]

You should keep simplifying

 

[braintic]

There won't be a question in the HSC that requires mindless expanding. For the sake of what is being tested, you've shown enough.