Graph x-1/8y^2=0

Problem

x−1/8*y2=0

Solution

1. Isolate the variable x to identify the form of the equation.

x=1/8*y2

2. Identify the type of conic section. Since the equation is in the form x=a*y2 it represents a parabola that opens horizontally to the right.

3. Determine the vertex. Since there are no horizontal or vertical shifts, the vertex is at the origin (0,0)

4. Find the focus and directrix using the standard form x=1/(4*p)*y2

1/(4*p)=1/8

4*p=8

p=2

5. Locate key features. The focus is at (p,0) which is (2,0) and the directrix is the vertical line x=−p which is x=−2

6. Calculate additional points to plot the curve. If y=4

x=1/8*(4)2

x=16/8

x=2

If y=−4

x=1/8*(−4)2

x=2

Final Answer

x=1/8*y2

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