Analyze this conic section to answer the questions below. \( x^{2}=12(y-2) \) Ellipse Circle Hyperbola Warabola A. choice. (Type an ordered pair.) B. The answer is undefined. 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.

We start with the equation   x² = 12(y – 2). Step 1. Rewrite in standard form: Recall that the standard form for a vertical parabola is   (x – h)² = 4p(y – k). Here we can see directly that   h = 0 and k = 2, with 4p = 12, so p = 3. Thus the conic is a parabola (the “warabola” choice in the list is a humorous way of saying “parabola”). Its vertex is at (0, 2). Step 2. About a and b: For ellipses or hyperbolas in standard form you have parameters “a” and “b” (the semi-axes), but in the case of a parabola the only parameter that appears is p (the distance from the vertex to the focus). Therefore, the parameters “a” and “b” are not defined for a parabola. Now answering the questions: • Type of conic section: Parabola (Choice: Warabola). • A. (Vertex as an ordered pair): (0, 2). • B. (What are the values of a and b?): Since the standard form for a parabola does not have “a” and “b,” the correct choice is:   C. The answer is undefined. Thus, the equation represents a parabola with vertex (0, 2); and since “a” and “b” are parameters used for ellipses and hyperbolas, they are not defined for this conic.