Analyze this conic section to answer the questions below. Circle Allipse Harabola Here is the center of this conic section? Select the correct choice below and fill in any answer boxes in your choice. Type an ordered pair.) What are the values of a and \( b \) for this conic section? Select the correct choice below and fill in any answer boxes in your choice. A. a does not have a value and \( b=\square \) B. a = \( \square \), and \( b \) does not have a value C. The answer is undefined.

To analyze the conic section, we need to identify which type it is (circle, ellipse, or hyperbola) and then determine the center and the values of \( a \) and \( b \). 1. **Identify the Conic Section:** - **Circle:** The general equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius. - **Ellipse:** The general equation is \(\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1\), where \((h, k)\) is the center, \(a\) is the semi-major axis, and \(b\) is the semi-minor axis. - **Hyperbola:** The general equation is \(\frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1\) or \(-\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1\), where \((h, k)\) is the center, \(a\) is the distance from the center to the vertices along the x-axis, and \(b\) is the distance from the center to the vertices along the y-axis. 2. **Determine the Center:** - For a circle, the center is \((h, k)\). - For an ellipse and hyperbola, the center is also \((h, k)\). 3. **Values of \( a \) and \( b \):** - For a circle, \( a \) does not have a value (since it is defined by the radius \( r \)), and \( b \) does not have a value. - For an ellipse, both \( a \) and \( b \) have values. - For a hyperbola, both \( a \) and \( b \) have values. ### Conclusion: - **Center:** The center of the conic section is \((h, k)\). - **Values of \( a \) and \( b \):** - If the conic section is a circle, the answer is A: \( a \) does not have a value and \( b \) does not have a value. - If it is an ellipse or hyperbola, we need specific values for \( a \) and \( b \). Please provide the specific equation or additional details about the conic section to determine the center and the values of \( a \) and \( b \).