In Exercise, use the techniques of Examples 1 and 2 to graph the equation in a suitable sq...

In Exercise, use the techniques of Examples 1 and 2 to graph the equation in a suitable square viewing window.

3x2 + 2y2 = 48

EXAMPLE 1

Graph the circle x2 + y2 = 9 on a calculator.

SOLUTION First, we solve the equation for y:

Graphing both of these equations on the same screen will produce the graph of the circle (Figure 1). However, the graph does not look like a circle because the standard window in Figure 1 is not square (a one-unit segment on the x-axis is a tad longer than a one-unit segment on the y-axis).

If we select Square (or ZSquare, ZSqr, ZoomSqr, or Sqr) in the ZOOM menu, the length of the x-axis is adjusted to produce a square window in which the circle looks round (Figure 2).* Alternatively, we can change the WINDOW settings by hand to obtain a square window such as Figure 3.†

Figure 1

Figure 2

Figure 3

*On HP-39gs, SQUARE adjusts the length of the y-axis to produce a square window.

†The gap between the top and bottom of the circle (more apparent here than in Figure 2) is caused by the low resolution of the calculator screen.

EXAMPLE 2

To graph 12x2 − 4y2 + 16x + 12 = 0, solve the equation for y:

Every point on the graph of the equation is on the graph of either