In Exercises 1–4, find the focus and directrix of each parabola w...

Question

In Exercises 1–4, find the focus and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d).x^2 = - 4y

Accepted Answer

Choose the correct option for the graph focus and direct of the parabola X squared equals negative A Y. Now we have four possible answers here. They all each have a graph pointing in a certain direction with this direct trick and focus plotted along with the equation of the direct trick and the point for the focus. Now to solve this, let's first look at the general form or standard form of a Parabola, we have X squared equals negative eight Y because we have X squared equals some number multiplied by Y. This is a vertically oriented Parabola which means it's going the point either up or down. In our case, it will point down based on our negative. The formula for this in standard form is X minus H squared equals four P multiplied by Y minus K where H K is our vertex. Now the equation for focus in a vertically oriented parabola, it is given by the point H K plus P. So we can solve for P from our equation, we notice four P multiplies R Y and also negative eight multiplies A Y in the equation which means we want four P is equal to negative eight which gives us P equals negative two. Our focus then is the point H K plus Pr H is zero. R K is also zero, meaning we get the 0.0 negative two for our focus, our direct tricks then will be an equation. Why equals K minus P when R K is zero and R P is negative two, which means we get the line Y equals two. For our directs. We now have our direct tricks and our focus. We know this graph should be pointing downwards. So the answer to our problem, if we go down, we see is answer D OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 1–4, find the focus and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d).x^2 = - 4y

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