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 − 4)²/9 + (y +2)² /25= 1

Equation of an ellipse in standard form: (x - 3)²/4 + (y + 1)²/16 = 1.

Accepted Answer

Graph, the given ellipse and indicate its pho where our equation is X minus three squared divided by four plus Y plus one squared, divided by 16 is equals to one. Now, we know the general form of an ellipse is X minus eight squared divided by A squared plus Y minus K squared divided by B squared is equals to one. We can then see our a squared, four B squared is 16. We also have our center was given by the point H K Where we can then see our point will be three negative one. Now we can find the end points of our ellipse and the side of the ellipse first and figure out what type of ellipsis is. We notice our B square is greater than a square. This means our lips is vertical. We can then find the end point vertically. We'll see pardon points vertically will be H K plus B and H OK minus B Our end points then will be 3 -1 plus our beef. What is four, three, negative one minus four and three negative one plus four. Our end points then Will be 3, 3 and three negative five. Now we define our both side are given by the linear eccentricity equation C is equals to the square root B squared minus A squared. We can find our sea square root of B squared. So 16 A minus A squared plus four, the C is equals to the square root of Which simplifies the two squares of three. Ahoy then occur at H K plus C N H K minus C three N one plus two squares of three M 3 -1 -2 Squares of three. We could then simplify to get three, 2.4, And 3 -4.464. We're given all the points we need. If you look at our possible answers, we can then determine our graph corresponds with graph D. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 37–50, graph each ellipse and give the location of its foci. (x − 4)²/9 + (y +2)² /25= 1

Key Concepts

Standard Form of an Ellipse

Foci of an Ellipse

Graphing an Ellipse

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