graph each equation.\n9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)\ngraph with x-axis from -8 to 8 and…
graph each equation.\n9) \\(\\frac{x^2}{4} + \\frac{y^2}{9} = 1\\)\ngraph with x-axis from -8 to 8 and y-axis from -8 to 8, grid lines
Answer
Explanation:
Step1: Identify ellipse standard form
The equation $\frac{x^2}{4} + \frac{y^2}{9} = 1$ matches $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$ ($a > b$), so it's a vertical ellipse with center at origin.
Step2: Calculate semi-axes
$a^2=9\Rightarrow a=3$, $b^2=4\Rightarrow b=2$.
Step3: Find vertices and co-vertices
Vertices: $(0,\pm3)$; Co-vertices: $(\pm2,0)$.
Step4: Plot points and draw ellipse
Mark $(0,3),(0,-3),(2,0),(-2,0)$ on grid, then connect smoothly.
Answer:
The graph is a vertical ellipse centered at the origin with vertices at (0, ±3) and co-vertices at (±2, 0). (Plot these points and connect to form the ellipse.)