Example 2

Sketch the curve 4x² + y² = 9 and find the foci. The equation may be rewritten as

The graph (Figure 5.5.5) is a vertical ellipse cutting the x-axis at ±3/2 and the y-axis at ±3.

Figure 5.5.5

By Theorem 1, the foci are on the y-axis at (0, ±c). We compute c from the equation

c² = b² - a²

a and b are the x and y intercepts of the ellipse, a = 3/2, b = 3. Thus

The foci are at (0, ±2.598).