In Exercises 25–36, find the standard form of the equation of eac...

Question

In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions. Foci: (0, -4), (0, 4); vertices: (0, −7), (0, 7)

Accepted Answer

find the equation of the ellipse with the following properties and express your answer and standard form. So we first need to figure out what direction this he lives is actually pointing in. He'll care. We have both sides from 0 -2-0 to you notice are both sides actually on the Y axis. Are vortices are also going on the Y axis. So this is the equation of the form X squared over p squared plus Y squared over A squared equals what It's no one to find both part A and RB. We can also find our sinner as well. So center, it's equal to the midpoint of our forces or verses. So look at this we will have, I'll use the midpoint of our cozy. We have zero plus 0/2 comma negative two plus two. Number two. Which side results in zero comma zero. So our center is 00. Now we want to go in and find what our A and B are A. Is the distance from the center to one of our vertex is We noticed there were on the Y axis. So our center 001 of our vertex is could be 08. Let's say zero comment eight zero. You want to find the distance. Other words, The distance will just be eight As we were eight away from the center. Now we're gonna find our B. To find our B. It will take B equals square root of a squared minus C squared. So you plug in our A 88 squared. Now you what R C squared. R C. Is actually equal to our fosse, the distance from the center to the far side. We can say that's too to sweat. RB isn't equal to the Square 64 -4, which is the square of 60. Now that we know what our A and B are, we can plug it into our formula. You have x squared over the square of 60 squared plus Y squared over eight squared equals what simplify even further. X squared over 60 plus one squared over equals what. Now. If you look at our answers, we can tell the answer to this problem is answer A. Okay. I hope that we solve the problem. Thank you for watching. Goodbye.

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In Exercises 25–36, find the standard form of the equation of each ellipse satisfying the given conditions. Foci: (0, -4), (0, 4); vertices: (0, −7), (0, 7)