Graph x^2=5y

Problem

x2=5*y

Solution

1. Identify the type of conic section. The equation x2=5*y is in the standard form of a parabola that opens vertically, x2=4*p*y

2. Determine the value of p to find the focus and directrix.

4*p=5

p=5/4=1.25

3. Locate the vertex. Since there are no h or k offsets, the vertex is at the origin.

Vertex=(0,0)

4. Find the focus and directrix. Since p is positive and the x term is squared, the parabola opens upward.

Focus=(0,p)=(0,1.25)

Directrix:y=−p⇒y=−1.25

5. Calculate additional points to define the width. Let y=5 to make the calculation simple.

x2=5*(5)

x2=25

x=±5

The points (5,5) and (−5,5) are on the graph.

6. Sketch the curve. Draw a smooth U-shaped curve passing through the vertex (0,0) and the points (5,5) and (−5,5) opening upward toward the focus.

Final Answer

x2=5*y⇒y=1/5*x2

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