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

Question

Find the standard form of the equation of the parabola satisfying the given conditions. Focus: (12,0); Directrix: x=-12

Accepted Answer

Hello today we're gonna be using the given information to find the equation of the parabola. So what we are given is a focus at negative three comma zero. And we are given a direct tricks which is represented by X. Is equal to three. Now, in order to find the equation of the parabola, let's just go ahead and graph what is given to us. So we are told that the focus is at negative three comma zero, so it lies negatively on the X axis and we are told that the direct tricks is that X is equal to three. So that is represented by a vertical line that is located at X is equal to three. Now the vertex of our parabola is always going to be the midpoint between our focus and our direct tricks notice that the direct tricks is that X is equal to three and the focus is at negative three. So we have a total distance Of six between the focus and the direct tricks and that means that the midpoint between these two pieces of information is going to be right at the origin of the Graph 000. Now the graph always opens up towards the focus here. The focus is at the negative portion of the x axis. So that means that the parabola is going to open up negatively towards the X axis. And that means that the general form of this Parabola is going to be represented by y squared is equal to negative for P X. Because this form here represents any Parabola that opens up negatively towards the X axis. Furthermore, P is the distance between the focus and the vertex here. The vertex is at 00 and the focus is at negative three. So the total distance between the focus and origin is going to be three. So in this case here P is equal to three and now we just need to go ahead and plug this into the general form of our parabola. Once again that's going to be Y squared is equal to negative four P. X. And again P is equal to three. So replacing P with three is going to give us y squared is equal to negative four times three times X. Negative four times three is going to give us negative 12. So we have y squared is equal to negative 12 X. And this is going to be the equation of the parabola with the given information. And that means that the answer to this problem is going to be C. 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

Find the standard form of the equation of the parabola satisfying the given conditions. Focus: (12,0); Directrix: x=-12

Key Concepts

Standard Form of a Parabola

Focus and Directrix

Vertex of the Parabola

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