graph each equation.\n9) \\(\frac{x^2}{4} + \frac{y^2}{9} = 1\\)\ncoordinate plane with x from -8 to 8 and y…

Explanation:

Step1: Identify the conic section

The equation (\frac{x^{2}}{4}+\frac{y^{2}}{9} = 1) is in the standard form of an ellipse, (\frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1) (since (a>b) for vertical major axis), where (a^{2} = 9) and (b^{2}=4). So (a = 3) and (b = 2).

Step2: Find the vertices and co - vertices

For a vertical ellipse centered at the origin ((0,0)):

• The vertices (endpoints of the major axis) are at ((0,\pm a)=(0,\pm3)).
• The co - vertices (endpoints of the minor axis) are at ((\pm b,0)=(\pm2,0)).

Step3: Plot the points

• Plot the vertices ((0, 3)) and ((0,- 3)).
• Plot the co - vertices ((2,0)) and ((-2,0)).

Step4: Draw the ellipse

Connect the plotted points smoothly to form the ellipse. The ellipse will be symmetric about both the (x) - axis and (y) - axis.

Answer:

The graph is an ellipse centered at the origin with vertices at ((0, 3)), ((0,-3)) and co - vertices at ((2,0)), ((-2,0)), drawn by connecting these points smoothly. (To actually draw it on the given grid, mark the points ((0,3)), ((0, - 3)), ((2,0)), ((-2,0)) and sketch the ellipse passing through these points, symmetric about both axes.)