Find the Properties x^2=4y

Problem

x2=4*y

Solution

1. Identify the type of conic section. Since the equation is in the form x2=4*p*y it represents a parabola that opens vertically.

2. Determine the value of p by comparing the given equation x2=4*y to the standard form x2=4*p*y

4*p=4

p=1

3. Locate the vertex. For the standard form x2=4*p*y the vertex is at the origin.

Vertex=(0,0)

4. Find the focus. Since the parabola opens upward (p>0, the focus is located at (0,p)

Focus=(0,1)

5. Determine the directrix. The directrix is a horizontal line located at y=−p

y=−1

6. Identify the axis of symmetry. For a vertical parabola centered at the origin, the axis of symmetry is the y-axis.

x=0

Final Answer

Properties of *x2=4*y:Vertex: *(0,0), Focus: *(0,1), Directrix: *y=−1, Axis of Symmetry: *x=0

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