Find the Properties y^2=4x

Problem

y2=4*x

Solution

1. Identify the type of conic section. The equation is in the form y2=4*p*x which represents a parabola that opens to the right.

2. Determine the value of p By comparing y2=4*x to the standard form y2=4*p*x we set 4*p=4 which gives p=1

3. Locate the vertex. Since there are no h or k offsets in the equation, the vertex is at the origin (0,0)

4. Find the focus. For a parabola opening right, the focus is at (p,0) Substituting p=1 the focus is (1,0)

5. Determine the directrix. The directrix is a vertical line given by x=−p Substituting p=1 the directrix is x=−1

6. Identify the axis of symmetry. The axis of symmetry is the line passing through the vertex and focus, which is the x-axis, y=0

7. Calculate the focal diameter (latus rectum length). the length is given by |4*p| which is |4*(1)|=4

Final Answer

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

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