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 be using the given information to find the equation of the parabola. So what we are told is that the focus is located at zero comma six. And we told that the direct tricks Is represented by the graph. Why is equal to -6? So let's just go ahead and start this by graphing what is given to us. So again the focus is at zero comma six which means it lies positively on the y axis. And we are told that the direct tricks is that y is equal to negative six. So we have this horizontal line located at Y is equal to negative six. Now the vertex of the Parabola is always going to be the midpoint between the focus and the direct tricks. Since the focus and the direct tricks have a total distance of 12, The vertex of the Parabola is going to lie in the middle of this which is six distance away and that's going to be right on the origin, 000. Now since the focus lies positively along the Y axis, that's an indication that we're going to have a parabola that opens up positively towards the y axis. And when we have a positive parabola opening up towards the y axis, that means that we're going to have the graph of the form X squared is equal to four py And that's because at this graph here represents any parabola that is a positively towards the y axis and starts at the origin of the graph. So here p is the distance between the focus and the origin or the vertex of the parabola and the distance between the focus and the vertex is going to be six. Because to go from 0 to 6 you need to travel a total distance of six. So for our graph, P is going to equal to six and now we just need to go ahead and plug that in to the general form of our equation. So we have X squared is equal to four P. Y. And since P is equal to six, what this gives us is x squared is equal to four times six times y. Four times six is going to give us 24. And that leaves us with X squared is equal to 24 Y. Which is going to be the equation of the graph of the parabola with are given information and that means that the answer to this problem is going to be B. So I hope this video helps you in understanding how to find the equation of the parabola and I'll go ahead and see you all in the next video

Struggling with College Algebra?

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

Watch next

Parabolas practice set