https://file.aiquickdraw.com/mathbot/file/1725928099019iejhuynq.jpg

To write the given equation for the hyperboloid of two sheets in standard form, we need to manipulate the given equation:

\[
-8x^2 + 9y^2 - 72z^2 - 72 = 0
\]

### Step 1: Move the constant term to the right-hand side.
\[
-8x^2 + 9y^2 - 72z^2 = 72
\]

### Step 2: Divide the entire equation by 72 to normalize the equation.
\[
\frac{-8x^2}{72} + \frac{9y^2}{72} - \frac{72z^2}{72} = 1
\]

### Step 3: Simplify each term.
\[
\frac{-x^2}{9} + \frac{y^2}{8} - z^2 = 1
\]

Now, the equation is in the standard form of a hyperboloid of two sheets:

\[
\frac{x^2}{9} - \frac{y^2}{8} + z^2 = -1
\]

Would you like further details or have any questions?

### Related Questions:
1. What is the general form of a hyperboloid of two sheets?
2. How does the standard form of a hyperboloid of one sheet differ?
3. What are the key properties of hyperboloids?
4. How can you derive the equation of a hyperboloid given certain dimensions?
5. How can the orientation of a hyperboloid be determined from its equation?

### Tip:
Always remember that a hyperboloid of two sheets has a standard form where the signs of two squared terms differ from the third.

Write the equation for the hyperboloid of two sheets given by -8x^2 + 9y^2 - 72z^2 - 72 = 0 in standard form.

Learn how to convert the equation of a hyperboloid of two sheets, given as -8x^2 + 9y^2 - 72z^2 - 72 = 0, into its standard form. This step-by-step guide covers essential algebraic techniques and conic section concepts, suitable for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation