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The question in the image is asking about the distance between the foci of the hyperbola given by the equation \( x^2 - y^2 = 18 \).

This equation is of the form:

\[
\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1
\]

We need to rewrite the given equation \( x^2 - y^2 = 18 \) in this standard form:

\[
\frac{x^2}{18} - \frac{y^2}{18} = 1
\]

Here, \( a^2 = 18 \) and \( b^2 = 18 \).

For a hyperbola, the distance between the foci is given by \( 2c \), where \( c \) is calculated using the formula:

\[
c^2 = a^2 + b^2
\]

Substituting the values of \( a^2 \) and \( b^2 \):

\[
c^2 = 18 + 18 = 36
\]

\[
c = \sqrt{36} = 6
\]

Thus, the distance between the foci is \( 2c = 2 \times 6 = 12 \).

The correct answer is **C) 12 একক**.

Would you like a further breakdown or explanation? Here are some related questions:

1. How do you identify the standard form of a hyperbola from its equation?
2. What are the foci of a hyperbola, and why are they important?
3. How does the distance between the foci relate to the shape of a hyperbola?
4. How would the equation change if it were a vertical hyperbola?
5. What would be the vertices' distance from the center of this hyperbola?

**Tip:** For any conic section, the relationship between the foci, vertices, and center is crucial for determining its shape and properties.

x^2 - y^2 = 18. অভিবৃত্তের কোলাদ্বয়ের মধ্যবর্তী দূরত্ব কত?

Learn how to calculate the distance between the foci of the hyperbola given by the equation x^2 - y^2 = 18. This problem covers key conic section concepts, including hyperbolas and their standard form. Suitable for students in Grades 11-12.

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