Answer:
Explanation:
To graph an ellipse with the given information, you can follow these steps:
Plot the center of the ellipse: (-2, -3).
Plot the focus point: (-19, -3).
Plot the vertex point: (6, -3).
Since the focus and the vertex points share the same y-coordinate, the major axis of the ellipse is horizontal. The distance between the center and the focus is called the focal length, denoted by c. The distance between the center and the vertex is called the semi-major axis, denoted by a.
Calculate the distance between the center and the focus:
c = |-2 - (-19)| = 17.
Calculate the distance between the center and the vertex:
a = |-2 - 6| = 8.
Now that you have the values for a and c, you can graph the ellipse based on these measurements. The horizontal axis length is 2a, and the vertical axis length is 2c.
Plot the points on the graph using the information calculated above.
Plot the center point: (-2, -3).
Plot the focus point: (-19, -3).
Plot the vertex point: (6, -3).
Draw a horizontal line segment through the center point with a length of 2a (16 units) to both the left and right. This will represent the major axis of the ellipse.
Draw two vertical line segments through the center point with a length of 2c (34 units) both above and below. These line segments will represent the minor axis of the ellipse.
Connect the ends of the major axis line segments to the corresponding ends of the minor axis line segments, forming an ellipse.