Find the standard form of the equation of the parabola satisfying...

Question

Find the standard form of the equation of the parabola satisfying the given conditions. Focus: (0,-11); Directrix: y=11

Accepted Answer

Hello today we're going to go ahead and find the standard equation of a parabola. When we are given a focus of zero comma six and a direct tricks of y is equal to negative six. So before we jump into this, let's just go ahead and recall the possible equations for our parabola. Now, if our parabola opens up or down, the form of that equation is going to be x squared is equal to four py and if our parabola opens up either to the left or to the right, the form of that equation is going to be y squared is equal to four, P. X. And P is going to be our focal constant. So in order to figure out which equation we're gonna be using, let's just go ahead and graph what is given to us so far. So we know that the focus is located at zero comma six and we know that the direct tricks is that why is equal to negative six? So if we graph what we are given, we know that the focus is going to be located on the y axis at zero comma six. And the direct tricks is going to be a horizontal line and why is equal to negative six. Well, since our focus is on the y axis in the positive direction, that means that the vertex of the actual parabola is going to be right below it and the parabola is going to need to open in the positive direction. So since our parabola is going to be opening up in the positive Y direction. The form of our graph or the form of our equation is going to be x squared is equal to four P. Y. Okay, so now we know the form of our equation but what we're missing is a value for P. Well in order to get that we just need to look at what the location of the focus is while the focus is located at six. So P is going to equal to six in order to find our equation. We're just gonna take this value of P and plug it in to our equation. Doing so is going to give us X squared is equal to four times six times Y and six times four is 24. So the graph, the equation of our graph is going to be x squared is equal to 24 Y. And that's gonna be our solution. That also means that the answer to this problem is going to be be. So I hope this video helps you in understanding how to find the graph of a parabola. And I'll go ahead and see you all in the next video

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