Question

graph each equation.

1. $\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$

Explanation:

Step1: Identify ellipse standard form

The given equation $\frac{x^2}{4} + \frac{y^2}{9} = 1$ matches the vertical major axis ellipse standard form $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$ where $a > b$.

Step2: Calculate semi-axes lengths

$a^2=9 \implies a=3$, $b^2=4 \implies b=2$

Step3: Find key intercept points

• x-intercepts: $(\pm b, 0) = (\pm 2, 0)$
• y-intercepts: $(0, \pm a) = (0, \pm 3)$

Step4: Plot and connect points

Mark the four intercepts on the grid, then draw a smooth closed ellipse passing through them.

Answer:

该方程表示以原点为中心，长轴在y轴上的椭圆，关键顶点为$(-2,0)$、$(2,0)$、$(0,3)$、$(0,-3)$，通过这些点绘制出光滑的闭合椭圆即可完成图像绘制。