Question

Find the center, the vertices, the foci, and the asymptotes. Then draw the graph. {(x−1)² / 9 }​ − {(y+3)² / 1​=1} The vertices are ______

Answer 1

The vertices of the given ellipse are (-2, -3) and (4, -3).

Step-by-step explanation:

To find the vertices of the given ellipse, we can compare the equation to the standard form: (x - h)^2/a^2 + (y - k)^2/b^2 = 1. The center of the ellipse is given by the coordinates (h, k), so in this case, the center is (1, -3).

The vertices of the ellipse are found by adding and subtracting the value of the semi-major axis, a, from the x-coordinate of the center. In this case, a = 3, so the vertices are (1-3, -3) and (1+3, -3), which simplifies to (-2, -3) and (4, -3).