In Exercises 5–16, find the focus and directrix of the parabola w...

Question

In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola.

8x^2 + 4y = 0

Accepted Answer

For the following equation of a Parabola solve for the focus in direct tricks. And then graph where we have 18 X squared plus nine Y equals zero. Now, to solve this, we need to turn it into the form of a Parabola. We have 18 X squared. That means our problem is the form X minus H squared equals four. A multiplied by Y minus K. This tells us we have a vertically facing. So let's transform our Parabola into the swamp to do this. We will just move our nine Y over to the right side giving us 18 X squared equals negative nine Y. Been dividing everything by 18 to get X squared equals negative one half Y. Now we know in our problem, our four a multiplies our Y, we will use a to find our focus in direct tricks. So let's set four A equals to negative one half, divide both sides by four and we get a equals negative one divided by eight. Now our focus will be the point H comma K plus A for a vertically oriented para you know, we don't have anything with our X or H will just be zero A K is also zero and we will add our A negative one X. Our focus is in zero, negative one eights. Now our direct tricks is the opposite direction of our focus. Because we set K plus A for our focus, our direct tricks will be Y equals negative A. You'll then get Y equals negative multiplied by negative 1/8. Give us Y equals 1/ for the direct tricks equaling one eights. Our focus being the 10.0 and negative one eights. Our answer turns out to be answer B which has this corresponding graph. OK? I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola. 8x^2 + 4y = 0