((x - 4) ^ 2)/12 - ((y + 3) ^ 2)/8 = 1 pada titik (-2, 1).

We have the equation \(\frac{(x - 4)^2}{12} - \frac{(y + 3)^2}{8} = 1\) and we need to check whether the point \((-2, 1)\) satisfies this equation.

To do this, we substitute \(x = -2\) and \(y = 1\) into the equation:

\[
\frac{((-2) - 4)^2}{12} - \frac{((1) + 3)^2}{8} = 1
\]

Let's calculate each term step by step:

1. \( (-2) - 4 = -6 \) 
   
   So, \( (-6)^2 = 36 \)

   Therefore, \(\frac{36}{12} = 3\).

2. \( 1 + 3 = 4 \)
   
   So, \( 4^2 = 16 \)

   Therefore, \(\frac{16}{8} = 2\).

Now substitute these values into the equation:

\[
3 - 2 = 1
\]

The equation holds true, so the point \((-2, 1)\) **does** satisfy the equation.

Would you like more details or have any questions? Here are five related questions to explore:

1. What is the geometric interpretation of this equation?
2. How do you find the center and axes of this hyperbola?
3. What are the asymptotes of this hyperbola?
4. How can you graph this hyperbola?
5. What is the standard form of a hyperbola equation?

**Tip:** Always double-check calculations when substituting values into an equation, especially in more complex expressions.

Explore how to verify the hyperbola equation ((x - 4)^2)/12 - ((y + 3)^2)/8 = 1 at the specific point (-2, 1). Follow a step-by-step solution involving conic sections and hyperbola formulas. Suitable for high school students.

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