Find the Properties x=1/4y^2

Problem

x=1/4*y2

Solution

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

2. Rewrite the equation in the standard form (y−k)2=4*p*(x−h) to identify the vertex (h,k)

y2=4*x

3. Determine the vertex (h,k) by observing that there are no shifts in x or y

(h,k)=(0,0)

4. Calculate the value of p by setting the coefficient of x equal to 4*p

4*p=4

p=1

5. Find the focus. Since the parabola opens to the right (p>0, the focus is at (h+p,k)

Focus=(0+1,0)=(1,0)

6. Determine the directrix using the formula x=h−p

x=0−1

x=−1

7. Identify the axis of symmetry, which is the horizontal line passing through the vertex and focus.

y=0

Final Answer

x=1/4*y2⇒Vertex: *(0,0), Focus: *(1,0), Directrix: *x=−1, Axis of Symmetry: *y=0

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