Well, in this one we're going to try to find, it's already in standard form, so this one what we want to do is we want to figure out what, this one we want to figure out what the center is, what the foci is, and what the directrix is. Alright, so the first thing I need to do is determine is this going to be a vertical or is this going to be a horizontal prep? It's going to be a vertical, right?
Very well. So, now the next thing we need to do is let's just go through the center. Remember the center, if you remember the formula, your center.
is h comma k. So for this problem, it's going to be negative 3 comma 1, right? Okay.
The next thing is we need to determine the focus. Well, the focus, alright, if you guys remember, since this is a vertical, I'm going to be adding the focus to my y coordinate of the center. So it's going to be h comma k plus p. So then I just added in this term p. How do I figure out what p was?
Well, remember in your equation, when I have x minus h and this minus 1, let's write it out, equals 4p y minus k. 4p is what we have right here. So I don't know what p is. So what I'm going to say is, I'll just say, well, negative 2 equals 4p, right?
That's in the same spot. I have negative 2 here and I have a 4p there. They're in the same spot, right? Do you guys understand that relationship you see there?
So now to find the value of p, I'll just divide by 4, and I get negative 1 half equals p. So, all I need to do to find my focus is I'm just going to plug in what my k value is, or just plug in p and my k. So my focus... Is going to be h which is negative 3 and then k which is 1 plus a negative 1 half which is Possible now, okay.
I just did 1 plus a negative 1 half right then to find the directrix The directrix is going to be very similar, but the directrix is now y equals k minus p. When you guys did your homework quiz, I was very detailed on making sure you guys write this as a line. Your directrix is a line, it's not a point. Your focus is your point, your directrix is your line.
So since it's vertical, I'm going to be having a horizontal line. So my y is going to equal k minus p. So now I just write in...
Y equals, and make sure you guys understand this, 1 minus a negative 1 half. Right? So therefore, my line is going to be Y equals 3 halves. And that's it. Now we found our center, our focus, and our directors.
Does that make sense? Probably at least find the P. The hard part about this is figuring out what that P is. Just make sure you get it into that same format. And then you can say, oh, 4p equals negative 2. Once you've found the p, the focus you add the p, the directrix you subtract.
And it just depends. Is it vertical or horizontal? When you have it vertical, you're adding and subtracting g or k. If it was horizontal like the last problem, you add and subtract to the h. That's it.