In Exercises 37–50, graph each ellipse and give the location of i...

Question

In Exercises 37–50, graph each ellipse and give the location of its foci. (x +3)²/9 + (y -2)² = 1

Accepted Answer

Graph, the given ellipse and indicate a where we have X plus one squared divided by 36 plus Y minus four squared, divided by four S equals to one. Now we notice here we have the general form of an ellipse. Since the A squared is under our X, we have a horizontally oriented ellipse which means our semi measure axis will be horizontal or on the X direction, we can then see our A squared will be 36 our B squared will be four. Now to graph this, we need to find the end points of the ellipse and the side of the ellipse, the end points to the lips and a horizontal point to the lips is given by H plus A comma K N H minus A K where H K is the center of the ellipse. Let's go ahead and find the end points. You know a squared is 36. This means our A will be equals to six. If we take the square root of both sides, the end points in will be from our sin. Our sinner being N 14, negative one plus six and -1 -6. We want our a value as well For the four in there, our end points then turned out to be positive faith four And -74. We can also find the focus of our lips by using linear eccentricity, which is given by C as equals to the square root A squared minus B squared. Now our A squared is 36 our B squared is four. So we will subtract those two numbers Given a square root of 32, which simplifies four squares of two are two focus or will then be H plus C K N H minus C K. Now we will take H plus C K Where H was equal to negative one native one Plus four Squares to two, four And Native 1 -4 squared to two. Or now we just need to simplify our radical. We're gonna put this in the calculator, our first one, negative one plus four square to two. OK. I'll write this down there 4.657 or for other point, We should get negative 6.657. Or now, if you want to look for a graph that has all of our points, we can then determine our graph will be graph A. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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In Exercises 37–50, graph each ellipse and give the location of its foci. (x +3)²/9 + (y -2)² = 1

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