Question

Z2 = 16x2 + 4y2 + 64 (a) Reduce the equation to one of the standard forms.

Answer 1

To reduce the equation to one of the standard forms, move the variable terms to one side, the constant to the other side, divide by the constant, and recognize that the equation is in the form of a hyperboloid of one sheet.

Step-by-step explanation:

To reduce the equation z2 = 16x2 + 4y2 + 64 to one of the standard forms, follow these steps:

1. First, move all the terms involving variables to one side of the equation and the constant to the other side:
2. z2 - 16x2 - 4y2 = -64
3. Next, divide the entire equation by -64 to get a standardized form:
4. z2/64 - x2/4 - y2/16 = 1
5. Finally, you can see that the equation is in the standard form of a hyperboloid of one sheet where A2 = 64, B2 = 4, and C2 = 16.