In Example 3, change y² − 14 to 14 − y² and then determine what type of curve is represented.

Data from Example 3

Identify the curve represented by 2x² + 12x = y² − 14. Determine the appropriate quantities for the curve, and sketch the graph. Writing this equation in the form of Eq. (21.34), we have

We identify this equation as representing a hyperbola, because A and C have different signs and B = 0. We now write it in the standard form of a hyperbola:

Thus, we see that the center (h, k) of the hyperbola is the point (−3, 0). Also, a = √2 and b = 2. This means that the vertices are (−3 + √2, 0) and (−3 − √2, 0), and the conjugate axis extends from (−3, 2) to (−3,−2). Also, c² = 2 + 4 = 6, which means that c = √6. The foci are (−3 + √6, 0) and (−3 − √6, 0). The graph is shown in Fig. 21.93.

Transcribed Image Text:

A = 2 2x² - y² + 12x + 14 = 0 Lc=-1