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: (-5, 0), (5, 0); vertices: (-8, 0), (8,0)

Accepted Answer

find the equation of the list with the following properties express your answer. In standard form we first need to figure out what standard form is and to do that we can determine which way our ellipse is facing. If we look here are both side happen on the X axis as well as Alvertis is that means we have a horizontal ellipse. So we can say our form is X squared over A squared plus Y squared over B squared equals what. Now I'm gonna figure out what are A and B are as well as our center. The center is just the middle of either are vortices or fosse. Now we notice here Are far from negative 3- verses go from negative 6-6 to find the midpoint of either one of those pairs of points. Let's say we use the fossa. Our X would be negative three plus three over to R Y B zero plus 0/2 Which gives us the center of 00. Let's go ahead and find what our A and R B. R. We can determine our A. By finding the distance from the center to the vertex. Have you noticed here? Our vertex for a Starting at 0? Our centre we're going 26. So in this sense is actually six because we're not moving at all on the way our beef, which we actually don't know yet. We'll have to make use of a formula. We'll take the square root of a squared minus C squared where C. Is our foes. Our focus You notice here from 0-3. We are three awake So R. C. is three. R. B. Is going to be equal to the square root of six squared minus three squared. That's just the square root 36 -9 which is the square root of 27. Now we have everything we need to fill. Help our formula. We have X squared over a squared, just six square plus Y squared over the square. 27 squared equals one. Get X squared over 36 plus Y squared over equals what. We cannot simplify any further. So this is our equation which means the answer to our problem. It's answer T. Okay. I hope to help you 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: (-5, 0), (5, 0); vertices: (-8, 0), (8,0)