Parabolas

Exercises 9-16 give equations of pa...

Question

Parabolas

Exercises 9-16 give equations of parabolas. Find each parabola's focus and directrix. Then sketch the parabola. Include the focus and directrix in your sketch.

x² = 6y

Accepted Answer

Find the focus and direct traits of the parabola given by Y2 equals 8 X, then sketch the parabola, clearly labeling both features on the graph. And we're also given a graph to plot our parabylon. Now, to solve this, we need to make use of the standard form of the parabola. In this case, this is Y2 equals 4 PX. Now we have Y2 equals 8 X. So let's first solve for P, which gives us the focal length. We can match and set 4 P equals 8 and divide 4 to get p equals 2. So then, this parabolas opening to the right. So, we can use. Our equation to find our focus being P 0 as our points. In this case, this is 20. Now we can find our directors. Our direct tricks. is then given as X equals -P. So we have X equals -2. Which is a vertical line. Now let's go ahead and graph. Now we can start at the vertex, and in this case, this vertex is at 00. Our focus is at 20. And our direct trix is that X equals -2, so we'll draw a dashed vertical line at -2. Now we can graph our parabola. We can use the lattice rectum to find the points. Since we know 4P is equals to 8, The last rectum's width is 8 units. So, from here, we will go from 2 on the X and go up 4 and down 4. We can now draw our parabola. Which is a right-facing parabola. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

ParabolasExercises 9-16 give equations of parabolas. Find each parabola's focus and directrix. Then sketch the parabola. Include the focus and directrix in your sketch.x² = 6y

Watch next

Parabolas

Exercises 9-16 give equations of parabolas. Find each parabola's focus and directrix. Then sketch the parabola. Include the focus and directrix in your sketch.

x² = 6y