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The image contains mathematical questions related to parabolas, ellipses, and hyperbolas, asking to determine their key features such as vertices, foci, and directrices. I will now work through one of the equations and provide detailed solutions for each.

Let’s start with the first equation:
\[
a. \ y = \frac{1}{4}x^2
\]
This is a standard form of a parabola.

### Steps to solve:

1. **Identify the type of equation:**
   The given equation \(y = \frac{1}{4}x^2\) is a parabola in the form \(y = ax^2\), which opens upwards since \(a > 0\).

2. **Find the vertex:**
   The vertex for any parabola in the form \(y = ax^2\) is at the origin \((0, 0)\).

3. **Find the focus:**
   The focus of a parabola is given by the formula \(\left(0, \frac{1}{4a}\right)\). Here, \(a = \frac{1}{4}\), so the focus is:
   \[
   \left(0, \frac{1}{4 \times \frac{1}{4}} = 1\right)
   \]
   Thus, the focus is \((0, 1)\).

4. **Find the directrix:**
   The directrix is the line \(y = -\frac{1}{4a}\). Substituting \(a = \frac{1}{4}\):
   \[
   y = -\frac{1}{4 \times \frac{1}{4}} = -1
   \]
   So, the directrix is the line \(y = -1\).

5. **Axis of symmetry:**
   The axis of symmetry for this parabola is the vertical line passing through the vertex, i.e., \(x = 0\).

### Summary for equation \(y = \frac{1}{4}x^2\):
- **Vertex:** \((0, 0)\)
- **Focus:** \((0, 1)\)
- **Directrix:** \(y = -1\)
- **Axis of symmetry:** \(x = 0\)

Would you like me to proceed with solving the next equations step-by-step?

Tentukan ciri-ciri dari parabola (sumbu simetri, puncak, fokus, direktris), elips (jenis elips, titik pusat, fokus, puncak, direktris, eksentrisitas), dan hiperbola (jenis hiperbola, titik pusat, fokus, puncak, direktris, asimtot) untuk beberapa persamaan.

Learn how to determine the key features of conic sections such as parabolas, ellipses, and hyperbolas, including vertices, foci, directrices, and asymptotes. This problem involves solving quadratic equations and conic section properties, suitable for high school students in Grades 10-12.

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